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ACT Math : Simplifying

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Example Questions

Example Question #1 : Simplifying

Solve for x when 6x – 4 = 2x + 5

Possible Answers:

1/4

9/4

Correct answer:

9/4

Explanation:

Solve by simplifying:

6x – 4 = 2x + 5

6x = 2x + 9

4x = 9

x = 9/4

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Example Question #51 : Variables

What is the value of the following equation if t = 3 $\displaystyle t = 3$ and $\displaystyle v = –4$ ?

$\small 2t^2+4vt+2v^2$ $\displaystyle \small 2t^2+4vt+2v^2$

Possible Answers:

$\displaystyle 12$

$\displaystyle 60$

$\displaystyle 50$

$\displaystyle 2$

Correct answer:

$\displaystyle 2$

Explanation:

Substitute the numbers 3 and –4 for t and v, respectively.

$\small 2(3)^2+4(-4)(3)+2(-4)^2$ $\displaystyle \small 2(3)^2+4(-4)(3)+2(-4)^2$

$\small 18+(-48)+32=2$ $\displaystyle \small 18+(-48)+32=2$

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Example Question #3 : How To Simplify Binomials

Simplify the following binomial:

$4x^2 + 16x - 4 - 2x^{2}$ $\displaystyle 4x^2 + 16x - 4 - 2x^{2}$

Possible Answers:

$\displaystyle x^2 + 8x - 2$

$\displaystyle 2x^2 - 4x +16$

$\displaystyle x^2 - 4x +4$

$\displaystyle x^2 + 4x - 4$

$\displaystyle x^2 + 8x -4$

Correct answer:

$\displaystyle x^2 + 8x - 2$

Explanation:

The equation that is presented is:

$4x^2 + 16x - 4 - 2x^{2}$ $\displaystyle 4x^2 + 16x - 4 - 2x^{2}$

To get the correct answer, you first need to combine all of the like terms. So, you can subtract the 2x^2 $\displaystyle 2x^2$ from the 4x^2 $\displaystyle 4x^2$ , leaving you with:

$\displaystyle 2x^2 + 16x - 4$

From there, you can reduce the numbers by their greatest common denominator, in this case, $\displaystyle 2$ :

$\displaystyle x^2 + 8x - 2$

Then you have arrived at your final answer.

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Example Question #2 : How To Simplify Binomials

Simplify the following binomial expression:

$\displaystyle 16x^2 - 14x + 12x - 8 + 2$

Possible Answers:

$\displaystyle x^2 - 8x - 3$

$\displaystyle 8x^2 + 2x -3$

$\displaystyle 8x^2 - x - 3$

$\displaystyle 4x^2 - 4x - 4$

$\displaystyle 2x^2 - 4x - 3$

Correct answer:

$\displaystyle 8x^2 - x - 3$

Explanation:

First, combine all of the like terms that you are able:

$\displaystyle 16x^2 - 2x - 6$

Then, reduce by the greatest common denominator (in this case, $\displaystyle 2$ ):

$\displaystyle 8x^2 - x - 3$

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Example Question #21 : Binomials

Simplify the following binomial:

$17x^{2} - 15x + 3x^{2 }+10x$ $\displaystyle 17x^{2} - 15x + 3x^{2 }+10x$

Possible Answers:

$\displaystyle 10x^2 - x$

$\displaystyle 5x(4x-1)$

5(4x-x) $\displaystyle 5(4x-x)$

$\displaystyle 5x^2 - 3x$

$\displaystyle 5x^2(4x-x)$

Correct answer:

$\displaystyle 5x(4x-1)$

Explanation:

The equation presented in the problem is:

$17x^{2} - 15x + 3x^{2 }+10x$ $\displaystyle 17x^{2} - 15x + 3x^{2 }+10x$

First you have to combine the like terms, i.e. combining all instances of x^2 $\displaystyle x^2$ and $\displaystyle x$ :

$\displaystyle 20x^2 - 5x$

Then, you can factor out the common $\displaystyle 5x$ to get your answer

$\displaystyle 5x(4x-1)$

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ACT Math : Simplifying

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Simplifying

Example Question #51 : Variables

Example Question #3 : How To Simplify Binomials

Example Question #2 : How To Simplify Binomials

Example Question #21 : Binomials

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