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ACT Math : How to evaluate algebraic expressions

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Example Question #11 : Evaluating Expressions

What is the value of $x$ that satisfies the equation $5(x+2)=12x-5$ ?

Possible Answers:

$-\frac{15}{17}$

$1$

$0$

$\frac{15}{7}$

$\frac{15}{11}$

Correct answer:

$\frac{15}{7}$

Explanation:

Distributing the 5 on the left side of the equation gives you $5x+10=12x-5$ .

Subtracting $5x$ from both sides of the equation gives you $10=7x-5$ .

Adding 5 to both sides of the equation gives you $15=7x$ .

Dividing each side of the equation by 7 gives you $\frac{15}{7}=x$ .

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Example Question #11 : Evaluating Expressions

If $\small a = 2$ and $\small b = 4$ , what is $\small -4(ab)^{3} + (3a - 2b)$ ?

Possible Answers:

$-2050$

$-2046$

$-32,770$

$2046$

$2050$

Correct answer:

$-2050$

Explanation:

$\small -4(2\times 4)^{3} + \left ( 3\times 2 - 2\times 4 \right )$

$\small -4(512) + (6-8)$

$\small -2048 -2$

$\small -2050$

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Example Question #12 : Evaluating Expressions

8 less than 4 times a number is 76. Find the number.

Possible Answers:

Correct answer:

Explanation:

4x - 8 = 76

4x = 76 + 8

4x = 84

$x = \frac{84}{4} = 21$

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Example Question #11 : Evaluating Expressions

Let x = 2 , y = 3 and z = 4 . Solve $zx^{y}$

Possible Answers:

Correct answer:

Explanation:

Substitute the given values into the variables to get:

$4(2^{3})= 4(8)= 32$

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Example Question #15 : Evaluating Expressions

Bob needs to order 700 candy bars from a warehouse. The website he is ordering from shows that the candy bars come in cases of boxes with candy bars in each box. It is not possible to order partial cases. What is the fewest amount of cases that Bob should order?

Possible Answers:

Correct answer:

Explanation:

The answer is .

Bob must order full cases, which contain boxes of candy bars with bars per box. This comes out to a total of 15*10= 150 candy bars per case. An order of cases comes out to 150*4= 600 candy bars which is not enough. However if he orders one more case, the total comes out to 150*5=750 candy bars which allows him to barely surpass his needed amount of 700 bars.

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Example Question #11 : How To Evaluate Algebraic Expressions

Solve for :

15x=-8(5-x)

Possible Answers:

-40/7

40/7

40/23

-40/23

Correct answer:

-40/7

Explanation:

The answer is -40/7 .

To solve this equation for , first distribute the to make the equation

15x= -40+8x . Next, subtract from both sides to leave you with 7x=-40 . Finally, divide both sides by to determine that x=-40/7 .

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Example Question #17 : Evaluating Expressions

If three chairs cost $\$ 57.00$ , what is the cost of chairs?

Possible Answers:

$\$ 39.00$

$\$ 3.80$

$\$ 20.00$

$\$ 19.00$

$\$ 38.00$

Correct answer:

$\$ 38.00$

Explanation:

The answer is $\$ 38.00$ .

If three chairs cost $\$ 57.00$ , each chair costs 57/3=19 . To determine the cost of two chairs, multiply $\$ 19.00 * 2=\$ 38.00$ .

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Example Question #11 : How To Evaluate Algebraic Expressions

Evaluate the expression z/(z+5) for z=7

Possible Answers:

7/12

12/7

-12/7

-7/12

Correct answer:

7/12

Explanation:

The answer is 7/12

To solve this expression subsitute for . This results in 7/(7+5) . Simplify to get 7/12 as the answer.

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Example Question #19 : Evaluating Expressions

If 40% of equals 8, then

Possible Answers:

400

200

100

Correct answer:

200

Explanation:

The equation can be set up as follows:

0.4x = 8

Solve for

x = 8/0.4 = 20

Now that we know the value of , we can plug it in to our final equation:

$0.5x^{}2 --> 0.5(20)^{}2$

$0.5x^{}2 \rightarrow 0.5(20)^{}2$

Remember, in this scenario, we must follow proper order of operations, where power is taken in consideration before multiplication.

In other words, 20 is squared first, giving 400.

In our last step, we multiple 400 by 0.5, giving our final answer: 200

*Note, the other answer choices generally consist of answers at other steps of the problem or answers arrived at when not following proper order of operations. Be careful when answering questions like these, as they often have other answer choices meant to catch your mistake on the ACT.

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Example Question #20 : Evaluating Expressions

If y = -2 , then what is

$(y^{}2 + 4)(-5y - 2)$ ?

Possible Answers:

Correct answer:

Explanation:

One can arrive to the answer two ways. They can either use FOIL then plug in for , or they can plug in for first, and then solve.

We recommend using the latter approach, as it saves more time, an important skill to recognize to be successful on the ACT.

By plugging in for , we have:

$((-2)^{}2 + 4)(-5(-2) - 2)$

Which simplifies to,

(4 + 4)(10 -2)

(8)(8) or

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ACT Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Evaluating Expressions

Example Question #11 : Evaluating Expressions

Example Question #12 : Evaluating Expressions

Example Question #11 : Evaluating Expressions

Example Question #15 : Evaluating Expressions

Example Question #11 : How To Evaluate Algebraic Expressions

Example Question #17 : Evaluating Expressions

Example Question #11 : How To Evaluate Algebraic Expressions

Example Question #19 : Evaluating Expressions

Example Question #20 : Evaluating Expressions

All ACT Math Resources

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