High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #6 : How To Solve Two Step Equations With Integers In Pre Algebra

Simplify:

\displaystyle 2x^{5} + 5x^5

Possible Answers:

\displaystyle 7x

\displaystyle 10x^{5}

\displaystyle 7x^5

\displaystyle 7x^{25}

Correct answer:

\displaystyle 7x^5

Explanation:

According to the laws of exponents, if you add you do not add the exponents. Therefore \displaystyle 5 +2 =7, and the variable term remains \displaystyle x^{5}. The answer is \displaystyle 7x^5.

Example Question #421 : High School Math

Solve for \displaystyle \small s.

\displaystyle 26-s=13

Possible Answers:

\displaystyle s=2

\displaystyle s=13

\displaystyle s=-39

\displaystyle s=39

Correct answer:

\displaystyle s=13

Explanation:

\displaystyle 26-s=13

Add \displaystyle \small s to both sides.

\displaystyle 26-s+s=13+s

\displaystyle 26=13+s

Subtract 13 from both sides.

\displaystyle 26-13=13+s-13

\displaystyle 13=s

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for \displaystyle \small n.

\displaystyle 6n+14=38

Possible Answers:

\displaystyle n=9

\displaystyle n=144

\displaystyle n=2

\displaystyle n=4

Correct answer:

\displaystyle n=4

Explanation:

\displaystyle 6n+14=38

Subtract 14 from each side.

\displaystyle 6n+14-14=38-14

\displaystyle 6n=24

Divide both sides by 6.

\displaystyle \frac{6n}{6}=\frac{24}{6}

\displaystyle n=4

Example Question #11 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for \displaystyle x if, \displaystyle 5x^{2}= 245.

Possible Answers:

\displaystyle x=\pm8

\displaystyle x=\pm7

\displaystyle x=\pm9

\displaystyle x=\pm5

Correct answer:

\displaystyle x=\pm7

Explanation:

To solve for  we must get all of the numbers on the other side of the equation of .

When solving a simple two-step equation we must remove the numbers that are interacting with  in this order: Addition/Subtraction, Multiplication/Division, Exponents.

To do this in a problem where  is being multiplied by a number, we must divide both sides of the equation by the number.

In this case the number is \displaystyle 5 so we divide each side of the equation by \displaystyle 5 to make it look like this \displaystyle \frac{5x^{2}}{5}= \frac{245}{5}

Our new problem will look like this \displaystyle x^{2}=49.

We then must solve the exponential equation.

To solve an equation with  we must take the square root of each side of the equation to get  by itself.

Doing this makes our problem look like \displaystyle \sqrt{x^{2}}=\sqrt{49}

Then we perform the square root to get the answer \displaystyle x=\pm7

Remember that \displaystyle (-7)^{2} can also equal \displaystyle 49 so our answer will be both positive and negative.

The final answer looks like \displaystyle x=\pm7.

Example Question #12 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for the value of \displaystyle \small e.

\displaystyle 6e+8=14

Possible Answers:

\displaystyle e=36

\displaystyle e=\frac{22}{6}

\displaystyle e=1

\displaystyle e=132

Correct answer:

\displaystyle e=1

Explanation:

\displaystyle 6e+8=14

We need ot work to isolate the variable using inverse operations.

Subtract \displaystyle \small 8 from both sides.

\displaystyle 6e+8-8=14-8

\displaystyle 6e=6

Divide each side by \displaystyle \small 6.

\displaystyle \frac{6e}{6}=\frac{6}{6}

\displaystyle e=1

Example Question #12 : How To Solve Two Step Equations With Integers In Pre Algebra

\displaystyle x+7=12*2

Solve for \displaystyle x.

Possible Answers:

\displaystyle 10

\displaystyle 31

\displaystyle 18

\displaystyle 17

\displaystyle 29

Correct answer:

\displaystyle 17

Explanation:

To solve \displaystyle x+7=12*2, start by simplifying the right side.

\displaystyle x+7=12*2

\displaystyle x+7=24

Now isolate \displaystyle x. This means we need to subtract \displaystyle 7 from both sides.

\displaystyle x+7-7=24-7

\displaystyle x=24-7

\displaystyle x=17

Example Question #13 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for X in the following equation: \displaystyle 3X+4=6X-11

Possible Answers:

\displaystyle -3

\displaystyle 2

\displaystyle 5

\displaystyle -5

\displaystyle 3

Correct answer:

\displaystyle 5

Explanation:

To solve for X, we must isolate X on one side of the equation.  In this case, we do this by subtracting 3X and adding 11 to both sides.

\displaystyle (3X-3X)+(4+11)=(6X-3X)+(-11+11)

\displaystyle 15=3X

 

We now have isolated X on one side of the equation, so we need only to reduce 3X to 1X.  We can do this by dividing both sides by 3:

\displaystyle (15/3=3X/3)=(5=X)

 

Example Question #14 : How To Solve Two Step Equations With Integers In Pre Algebra

\displaystyle x-12=18+7

Solve for \displaystyle x.

Possible Answers:

\displaystyle 37

\displaystyle 27

\displaystyle 3

\displaystyle 13

\displaystyle 23

Correct answer:

\displaystyle 37

Explanation:

To solve for \displaystyle x, we need to isolate our variable. That means that we want ONLY the \displaystyle x on the left side of the equation. But first, we need to combine our like terms on the right side.

\displaystyle x-12=18+7

\displaystyle x-12=25

Add \displaystyle 12 to both sides.

\displaystyle x-12+12=25+12

\displaystyle x=25+12

\displaystyle x=37

Example Question #421 : High School Math

Solve for \displaystyle x if, \displaystyle 9x+44=125

Possible Answers:

\displaystyle 10

\displaystyle 11

\displaystyle 9

\displaystyle 8

Correct answer:

\displaystyle 9

Explanation:

To perform a two-step algebra problem with addition and multiplication we must remove the numbers from  so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being added so we must subtract the number, \displaystyle 44, from each side of the equation \displaystyle 9x+44-44=125-44

Perform the math so our equation becomes \displaystyle 9x=81

Then we divide each side of the equation by the number that is in front of \displaystyle 9, to get  by itself \displaystyle \frac{9x}{9}=\frac{81}{9}

Perform the math to find the answer \displaystyle x=9

Example Question #16 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for  if

\displaystyle \frac{x}{2}-15=75

Possible Answers:

\displaystyle x=175

\displaystyle x=45

\displaystyle x=150

\displaystyle x=180

Correct answer:

\displaystyle x=180

Explanation:

To perform a two-step algebra problem with addition and division we must remove the numbers from  so it is by itself on one side of the equation.

To do this we first look to see if a number is being added or subtracted from .

In this case a number is being subtracted so we must add the number, \displaystyle 15 , to each side of the equation 

\displaystyle \frac{x}{2}-15+15=75+15

Perform the math so our equation becomes

\displaystyle \frac{x}{2}=90

Then we multiply each side of the equation by the number that is under  to get  by itself 

\displaystyle 2\cdot \left(\frac{x}{2}\right)=(90)\cdot 2

Perform the math to find the answer \displaystyle x=180

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