ACT Math : How to evaluate algebraic expressions
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Example Questions
Example Question #2431 : Act Math
If x = y – 3, then (y – x)3 =
–9
27
9
3
–27
27
Solve for equation for y – x = 3. Then, plug in 3 into (y – x)3 = 27.
Example Question #2432 : Act Math
When graphed in the (x,y) coordinate plane, at what point do the lines -2x + 4y = 5 and y = -2 intersect?
(2,-2)
(-13/2,-2)
(13/2,2)
(13/2,-2)
(-13/2,-2)
Plugging in y=-2 in the second equation, gives x=-13/2. This is the point where the graphs intersect.
Example Question #1 : How To Evaluate Algebraic Expressions
The length in cm of a plastic container is 5cm less than triple its width. Which of the following equations is an accurate description of the length, l, as a function of the width, w?
l = 3w + 5
l = 1/3w – 5
l = 1/3w + 5
l = 3w – 5
l = 5/3w + 3/5
l = 3w – 5
This problem requires the development of an equation. We are told that the length is 5cm less than 3 times its width. So we should set up an equation that describes this situation. The equation l = 3w – 5 demonstrates how the length is 5 cm less than 3 times the width of the container.
Example Question #2434 : Act Math
The expression x(9 + x)(x – 2) = 4 is a polynomial of which degree?
0
2
3
4
1
3
The highest power this polynomial can achieve is 3.
Example Question #2435 : Act Math
Given that x = 2 and y = 3, how much less is the value of 3x2 – 2y than the value of 3y2 – 2x?
29
1
17
6
47
17
First, we solve each expression by plugging in the given values for x and y:
3(22) – 2(3) = 12 – 6 = 6
3(32) – 2(2) = 27 – 4 = 23
Then we find the difference between the first and second expressions’ values:
23 – 6 = 17
Example Question #1 : Evaluating Expressions
Evaluate 4x2 + 6x – 17, when x = 3.
37
30
13
17
36
37
Plug in 3 for x, giving you 36 + 18 – 17, which equals 37.
Example Question #1 : How To Evaluate Algebraic Expressions
John has a motorcycle. He drives it to the store, which is 30 miles away. It takes him 30 minutes to drive there and 60 minutes to drive back, due to traffic. What was his average speed roundtrip in miles per hour?
30 mph
45 mph
50 mph
40 mph
60 mph
40 mph
The whole trip is 60 miles, and it takes 90 minutes, which is 1.5 hours.
Miles per hour is 60/1.5 = 40 mph
Example Question #941 : Algebra
If (xy/2) – 3w = –9, what is the value of w in terms of x and y?
3xy + 6
(1/3)xy + 6
(1/2)xy – 3
w = 3 + (xy/6)
3xy – 6
w = 3 + (xy/6)
–3w = –9 – (xy/2)
w = 3 + (xy/6)
Example Question #2439 : Act Math
Evaluate 5x2 + 16x + 7 when x = 7
364
362
363
365
361
364
Plug in 7 for x and you get 5(49) + 16(7) + 7 = 364
Example Question #2440 : Act Math
Let 
In order to solve the expression, replace 
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