Solving Two-Step Equations
a = this when 39 = 15a + 24 Justify your answer by showing your work
What is a = 1
39 - 24 = 15a + 24 - 24
15 = 15a
15/15 = 15a/15
a = 1
Twice a number decreased by eight is sixteen.
What is 2m - 8 = 16
w = this when -5(2w + 1) = 25
What is w = -3? -10w - 5 = 25
-10w - 5 + 5 = 25 + 5
-10w = 30
-10w/-10 = 30/-10
w = -3
u = this when 25u + 74 = 23u + 92
What is u = 9? 25u + 74 = 23u + 92
25u - 23u + 74 = 23u - 23u + 92
2u + 74 - 74 = 92 - 74
2u/2 = 18/2
u = 9
This is the perimeter of a square when one side = 4r and the other side = 36 - 5r
What is r = 4 and the perimeter = 64?
k = this when 19k - 34 = 23 Justify your answer by showing your work
What is 3?
19k - 34 = 23
19k - 34 + 34 = 23 + 34
19k = 57 19k/19 = 57/19
k=3
Four times a number decreased by ten is thirty-two.
What is 4(m - 10) = 32?
h = this when -12 = -2h + 0.2(20 - 6h)
What is h = 5? -12 = -2h + 0.2(20 - 6h)
-12 = -2h + 4 - 1.2h
-12 - 4 = -3.2h + 4 - 4
-16 = -3.2h -16/-3.2 = -3.2h/-3.2
5 = h
k = this when -5k - 19 = 5 - 13k
What is k = 3? -5k - 19 = 5 - 13k
-5k + 13k - 19 = 5 - 13k + 13k
8k - 19 = 5
8k - 19 + 19 = 5 + 19
8k/8 = 24/8 k = 3
This is the perimeter of a square when one side = 2b and another side = b + 4.
What is b = 4 and the perimeter is 32 units?
n = this when 59 - 4n = 91 Justify your answer by showing your work
What is n = -8?
59 - 4n = 91
59 - 59 - 4n = 91 - 59
-4n = 32 -4n/-4 = 32/-4
n = -8
Thirty four decreased by four times a number is eighteen.
What is 34 - 4y = 18?
f = this when 42 = 18f + 4(f + 5)
What is f = 1? 42 = 18f + 4(f + 5)
42 = 18f + 4f + 20
42 - 20 = 22f + 20 - 20
22/22 = 22f/22
1 = f
p = this when 7(2p + 1) = 14p + 7
What is p = all numbers? 7(2p + 1) = 14p + 7
14p + 7 = 14p + 7
p = all numbers
This is the perimeter of the square when 3g = 2g + 3
What is g = 3 and the perimeter = 36 units?
m = this when m/8 + 12 = -5 justify your answer by showing work
What is m= -136? m/8 + 12 = -5
m/8 + 12 - 12 = -5 - 12
m/8 = -17 m/8 x 8 = -17 x 8
m = -136
Twelve less than -9 times a number is negative 60
What is -9k - 12 = -60?
z = this when -3(2z - 8) + 10z = 16
What is z = 2? -3(2z - 8) + 10z = 16
-6z + 24 + 10z = 16
4z + 24 - 24 = 16 - 24
4z/4 = -8/4
z = -2
m = this when 25m = 5(5m + 1)
What is m has no solution? 25m = 5(5m + 1)
25m = 25m + 5
25m - 25m = 25m - 25m + 5
0 = 5 no solution
This is the value of w when the perimeter of the square = 32 units and each side = w + 3
What is w = 5? 32 = 4(w + 3)
32 = 4w + 12
32 - 12 = 4w + 12 - 12
20/4 = 4w/4
5 = w
d = this when -8 = -14 - d/9 Justify your answer by showing your work
What is d = -54? -8 = -14 - d/9
-8 + 14 = -14 + 14 - d/9
6 = -d/9 6 x -9 = -d/9 x -9
-54 = d
Negative 8 minus the product of 3 and a number is 19.
What is -8 - 3v = 19?
g = this when -5g - (8 - g) = 12
What is g =
This is the equation and solution for the following verbal sentence:
three less than 11 times a number is equal to 9 plus 5 times the number
What is 11n - 3 = 9 + 5n and n = 2?
11n - 5n - 3 = 9 + 5n - 5n
6n - 3 + 3 = 9 + 3
6n/6 = 12/6
n = 2
This is the perimeter of a square whose one side = 12z and another side = 7z + 30
What is 288 units and z = 6?