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the mathematical reasoning section on theged is going to test your ability on solving algebraic equations. here is an example ofa question that you might have to solve when you take the ged. "if '10x' plus two equalsseven, what is the value of '2x'?" well, let's first start with solving this algebraic equationof "10x" plus two equals seven. because if we can figure out what "x" is, then we canfigure out what "2x" is. the first thing we need to do is subtract two from both sidesto get rid of this plus two. so, that leaves us with "10x" equals five. now to solve for"x", we undo the ten times "x" by dividing both sides by ten. ten divided by ten is one.so this is "x" equals, and you can simplify five-tenths to a half, or five-tenths. nowbe careful. because they didn't ask what is

the value of "x". they didn't ask you justto solve for "x", and they're expecting you not to pay attention. see this first answer?they're expecting you to solve for "x" and go "oh great there is my answer". so pay attentionto what they're asking. they want "2x", which means two times a half. and two times a halfis one. so, this answer would be c. so, this is something that you're going to have toknow how to do when you take the ged. the ged will test your knowledge of functionsand patterns. here is an example of the type of problem you'll see when you take the ged."which of the following equations satisfies the five sets of numbers shown in the abovetable?" you could start by seeing if you can figure out the pattern. meaning, what do youdo to "x" to get "y". so, just starting with

the first set, you could multiply negativetwo times two to get negative four. but it doesn't work on your next set of numbers.three times two is not thirty-one. you could also subtract two from negative two to getnegative four. but you can't subtract two from three to get thirty-one. so, it may bemore difficult to find the pattern in the table. luckily though, you have options. sinceyou have multiple-choice options, you can use these answer choices to test them againstyour table of values. that's the way we're going to approach this problem. let's startwith the first answer. "y" equals "2x" squared plus seven. now we just need to pick one setof numbers to substitute into this equation to test and see if that, if this equationdoes satisfy our set of numbers. so, let's

just take two and twelve. you could pick anyset you wanted, but i usually like to pick one that looks a little easier, like two andtwelve. the "y" is twelve, so replace "y" with twelve. we're checking to see if it equalstwo times the "x", which is two, squared plus seven. now it's really important that youfollow the order of operations when simplifying this right side. and there's a cute littleway to remember the order of operations which you may have heard, and that is pemdas. thep stands for parenthesis. the e stands for exponents. the m stands for multiplication,i'll just use the times dot. the d stands for division. the a stands for addition. andthe s stands for subtraction. so, that's the order that we have to simplify expressions.on this equation, we're going to start then

with our exponents. because, even though yousee parenthesis there, that's not actually what that p means. what is actuallymeans is grouping symbols, and we have nothing grouped inside the parenthesis. so in thiscase, the parenthesis are actually just a multiplication sign. so, we start right herewith two squared. and we have does twelve equal two times four plus seven. now we havemultiplication and addition. multiplication comes before addition. so, does twelve equaleight plus seven? and lastly, we add and we see that twelve does not equal fifteen, whichmeans this is not our answer. because that equation does not satisfy our set of numbers.now let's try b; "y" equals "x" cubed plus four. so that was a, let's try b. and we canjust use the same "x" and "y". so, i'm going

to replace the "y" again with twelve, andreplace the "x" again with two. follow your order of operations, which means exponentsfirst. two cubed is two times itself three times. so, two times two times two, whichis eight. and again we are checking to see if these are equal. eight plus four is twelve.so, twelve equals twelve. that doesn't necessarily mean that that's our answer though. just becauseit worked on one set of numbers, doesn't mean it will work on all of our sets of numbers.so, we need to keep testing answers. let's try c; "y" equals "2x". same "x" and "y".so, replace "y" with twelve and see if that equals two times "x" which is two. well twelvedoes not equal four, which means we can eliminate that as a possible answer choice. now let'stry d; "y" equals "3x" plus one. same "x"

and "y". so, twelve equals three times twoplus one. continue to follow your order of operations, so multiply first. we want tosee does twelve equal six plus one. twelve does not equal seven; therefore, that is alsonot our answer. let's try e now; "y" equals "6x". again "y" is twelve. we want to seeif that equals six times two. twelve does equal twelve. so, this is what i was talkingabout. because you can have more than one equation that works on one set of numbers.so, to determine which one is the correct answer, we need to test another ordered pair.so, let's just pick another set of numbers. um again, you want to keep it easy. you don'twant it to be too hard. how about negative two and negative four. so, i'm going to trythe same equation again but using another

set of numbers. so, this time the "y" is negativefour. we want to see if that equals negative two cubed plus four. still following the orderof operations, which means exponents first. negative two times negative two times negativetwo is negative eight plus four. and negative eight plus four is negative four. so, we weren'tsure if it equaled each other until it didn't, um in the end. so, this has helped confirmthat b is our answer. but we're not quite ready to circle it yet, until we determinethat e definitely isn't the answer. so, we're going to plug in the same ordered pair intothis answer choice e. so, again your "y" is negative four and we want to see if that equalssix times negative two. does negative four equal negative twelve? no. so that right thereconfirms that b is the correct answer because

e did not work when we tried another set ofnumbers. there you have an example of a problem using functions or patterns that you couldsee when you take the ged. if you're about to take the ged, then youneed to be prepared for word problems. here i have an example of the type of problem thatyou'll see when you take the ged. "a number n is multiplied by three. the result is thesame as when n is divided by three. what is the value of n?" well, i'm going to startby taking all these words and turning them into an equation. so, first we have n multipliedby three. and you would just write that as "3n" because that means three times n. thenthey say "the result is the same as". well, that's just saying equal to. so, equals, whenn is divided by three. and that is written

as n divided by three. then they ask, whatis the value of n. well, a couple of ways to do this. since you have the multiple-choiceanswers, you could use those. replace n with each answer, and figure out which value ofn makes this equation true. for example if you try one, you have three, replace n withone, times one equals, and you should put a question mark there because we're not sureif it's equal yet, one divided by three. three times one is three. and we want to know doesthree equal a third. well, no. three wholes and one-third of one whole are not the same.so, since these aren't equal, that means one is not the value of n. and you can do thatwith each answer choice until you find the one that does make the equation true. or youcan solve the equation. and there's more than

one way to solve the equation. you could divideboth sides by three, but then that might look kind of weird, since you already have n dividedby three. so, what i'll do is undo dividing n by three by multiplying both sides by three.so, three times "3n" is "9n". and that's equal to, these threes cross-cancel, just n. now,you have variables on both sides. so, we want to get all of our variables on one side. andyou can do that by subtracting n from both sides. you have nine ns minus an n leaves you witheight ns equals, n minus n is zero. now, to solve for n, we just divide both sidesby eight. so, n is equal to zero divided by anything is zero. so, there you have n iszero. let's test that out by plugging it back into our equation. so again, our equationis "3n" equals n divided by three. and since

we solved our equation, and got that n waszero, we're going to replace both of these ns with zero. so, three times zero, and wewant to see if it equals zero divided by three. zero times anything is zero. and zero dividedby anything is zero. and zero does equal zero. so, we found our answer, that n is zero. thereyou have one example of the type of problem you'll see when you take the ged.if you're taking the ged, you need to be prepared to answer word problems. and you're goingto have to have some knowledge of percentages as well. here's a problem that combines bothof those skills: word problem, it's a word problem, and you have to be able to use percentagesto solve it. "a long distance runner does a first lap around a track in exactly fiftyseconds. as she tires, each subsequent lap

takes twenty percent longer than the previousone. how long does she take to run three laps?" well first of all, if it takes her fifty secondsfor the first one, and she's running three, then that means fifty times three. it's goingto take her, at least, a hundred fifty seconds. you can already eliminate answer choice d.and since it's taking her longer for the other ones, meaning more than fifty seconds, thatmeans it's going to take more than fifty times three, or more than one hundred fifty seconds.so, we can eliminate e as well. we've already narrowed it down. so, our chances of gettingthis correct are even better now. so, let's lay out what we know. the first lap took herfifty seconds. the second lap took twenty percent longer than that. so, the second laptook her the fifty seconds, like the first

lap did, and twenty percent of fifty seconds.okay, we're going to have to do a little bit of translating here. we don't use percentageswhen we're calculating things. so, we leave this fifty, but we're going to change thispercent into a decimal. and the way to do that is to take the decimal in twenty percentand move it two places to the left. so, it's two-tenths. and then "of" tells you to multiply.so, we're going to multiply that two-tenths times fifty. so, we have fifty plus, two timesfifty is a hundred, and then there's one number behind the decimal. so, it took her ten secondslonger. because twenty percent of fifty is ten, and it took her ten seconds longer thanthe fifty seconds for the first lap. so, her second lap took her sixty seconds. the thirdlap we'll do similarly. it took, again, twenty

percent longer than, and this is key here,than the previous one. so, it's not going to be another sixty second lap. it took hersixty seconds and twenty percent of sixty seconds. so, sixty plus, again change thatto a decimal, so it's two-tenths, "of" tells you to multiply, so times sixty. so, sixtyseconds plus, two times sixty is one hundred twenty, and there's one number behind thedecimal. so, sixty plus twelve, or seventy-two seconds. now, since we're finding how longit took her to run all three laps, we need to take each one of these times and add themtogether. so, we have fifty for the first lap, sixty for the second lap, and seventy-twofor the third. that's two, seven plus six is thirteen, plus five is eighteen. so, ittook her one hundred eighty-two seconds to

do all three laps, answer b. so, this is justone example of the type of problem you're going to see when you take the ged.if you're taking the ged, be prepared for a lot of word problems, like this one. "johnbuys a hundred shares of stock at a hundred dollars per share. the price goes up by tenpercent and he sells fifty shares. then, prices drop by ten percent and he sells his remainingfifty shares. how much did he get for the last fifty?" okay so, here's what we're focusedon, just the last fifty. but we need to figure out what the price was of those last fiftyhe sold. so, it started at a hundred dollars per share, which we see right there. thenit increased by ten percent, it went up by ten percent. so, we're going to add ten percentto this hundred dollars. and ten percent of

a hundred dollars is ten dollars. so, thenew price, after it went up, was a hundred ten dollars. um, and let me show you, first,how to find the ten percent of a hundred dollars. this is how i find ten percent of anything.basically, ten percent of a number is just dividing that number by ten. and you can dividea number by ten by taking the decimal and moving it one place to the left. so, that'syour ten dollars. and you can do that with any number, just move the decimal one placeto the left and that's ten percent of that number. okay so, this was the price afterit increased by ten percent, but then, the prices dropped by ten percent. so, ten percentof a hundred ten dollars, again we find it the same way, just take that decimal, moveit one place to the left, and that's ten percent

of a hundred ten. since it dropped, we subtractthe eleven dollars from the hundred ten dollars, which is ninety-nine dollars. now, we canfinally find how much he sold those fifty shares for. he sold each share for ninety-ninedollars. so, it's ninety-nine times fifty, which is four thousand nine hundred fiftydollars. so, there you have one example of the kind of word problems you're going tosee when you take the ged. good luck!