ACT Math : How to evaluate algebraic expressions
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Example Questions
Example Question #21 : Evaluating Expressions
What is the value of z that satisfies the equation: 10(z – 6) = 8z + 4
–32
28
34
5
32
32
Distribute: 10z – 60 = 8z + 4
Move all like terms together: 2z = 64
Solve: z = 32
Example Question #21 : How To Evaluate Algebraic Expressions
If 
Divide both sides by 
Example Question #23 : Evaluating Expressions
Find the value of 
This problem requires utilization of the opposite operations to both sides principle.
Adding +2 to both sides yields
Subtracting 2y from both sides yields
Example Question #22 : How To Evaluate Algebraic Expressions
Sally is ordering snacks for her class trip. She needs 85 cookies. The cookies come in cases of 6 boxes, with 7 cookies in each box. Sally can't order a partial box. What is the smallest number of cases she should order?
6
2
3
1
4
3
We first determine how many cookies are in each box. There are 7 cookies in a box, multiplied by 6 boxes, making 42 cookies in a case. We then divide the total number of cookies she needs, 85, by the number in each case, 42, giving us 2 with a remainder. This means Sally must order 3 cases of cookies.
Example Question #23 : How To Evaluate Algebraic Expressions
A company rents cars for a rental fee of $37.00 per day, with an additional charge of $0.45 per mile driven. Which of the following expressions represents the cost, in dollars, of renting the car for 2 days and driving it m miles?
37m + 0.45
37m + 45
0.45m + 74
74m + 45
0.45m + 37
0.45m + 74
To determine cost we add the initial rental fee of $37, times two days giving us $74 plus the mileage rate, 0.45, times the number of miles. Giving an equation of 0.45m+74.
Example Question #61 : Expressions
If 
Substituting x+y for 5, we get
6(5) - 52 + (1/5)(5) + 8
30 - 25 + 1 + 8
= 14
Example Question #62 : Expressions
A batting average is determined by calculating the amount of hits a batter accumulates in the amount of at-bats that they have had in a season. However when a batter walks the at-bat is not counted in the calculation of the batter's batting average. Walks also have no effect on a batter's hit count.
Let:
Total at-bats, including times a batter has walked = a
Number of hits = b
Number of walks = c
What is an appropriate expression for the calculation of a hitter's batting average?
To conform to the way in which a batting average is calculated the equation must be set up so that the amount of hits a batter has accumulated is divided by the amount of at-bats the batter has had, without including at-bats that have resulted in a walk. So the equation should be (hits)/((at-bats) – (walks)), this is acheved by b/(a – c).
Example Question #27 : Evaluating Expressions
If st – 4r = 8, what is the value of t in terms of r and s?
(4s + 8)/r
s(4r + 8)
(8 – 4r)/s
(4r + 8)/s
(8 – 4s)/r
(4r + 8)/s
We rearrange the equation st – 4r=8 by adding 4r to the right side; then divide by s → t = (4r + 8)/s
Example Question #63 : Expressions
Which of the following is equal (10 – 6)2 if x = 10?
(x – 8)(x – 2)
(x + 6)(x – 6)
(x + 8)(x + 2)
(x + 4)(x – 4)
(x + 6)(x – 4)
(x – 8)(x – 2)
First, you set up and solve the original equation. Set up (10 – 6)2, then solve it, giving you 16. We can then plug in 10 for x in the answer choices until you find the choice that always gives you 16, which is (x – 8)(x – 2).
Example Question #64 : Expressions
If 
The value of 
Note that 
Since 
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