Answer:
Question 1: A. {-500}
Question 2: D. {-11}
Question 3: B. {2}
Question 4: A. {-19}
Question 5: A. {6}
Question 6: D. {23}
Question 7: B. {12}
Question 8: B. {-18}
Question 9: B. {-21}
Question 10: A. {-29}
Step-by-step explanation:
Question 1: [tex]\frac{b}{20}[/tex] = -25
Steps:
[tex]\frac{b}{20}[/tex] = -25
Multiply both sides by 20
[tex]\frac{20b}{20}[/tex] = 20 (-12)
Simplify
b = -500
Answer is A. {-500}
Question 2: 35 = 24 - b
Steps:
35 = 24 - b
Add b to both sides
35 + b = 24 - b + b
Simplify
35 + b = 24
Subtract 35 from both sides
35 + b - 35 = 24 - 35
Simplify again
b = -11
Answer is D. {-11}
Question 3: 24 = 22 + x
Steps:
24 = 22 + x
Switch sides
22 + x = 24
Subtract 22 from both sides
22 + x - 22 = 24 - 22
Simplify
x = 2
Answer is B. {2}
Question 4: -17x = 323
Steps:
-17x = 323
Divide both sides by -17
[tex]\frac{-17x}{-17}[/tex] = [tex]\frac{323}{-17}[/tex]
Simplify
[tex]\frac{-17x}{-17}[/tex]
Apply the fraction rule: For example, [tex]\frac{a}{-b}[/tex] = - [tex]\frac{a}{b}[/tex]
[tex]\frac{-17x}{-17}[/tex] = [tex]\frac{17x}{17}[/tex]
Divide the numbers
[tex]\frac{17x}{17}[/tex] = x
Simplify
[tex]\frac{323}{-17}[/tex]
Apply the fraction rule
[tex]\frac{323}{-17}[/tex] = - [tex]\frac{323}{17}[/tex]
Divide the numbers
[tex]\frac{323}{17}[/tex] = -19
x = -19
Answer is A. {-19}
Question 5: 4 = 10 - x
Solve:
4 = 10 - x
Add x to both sides
4 + x = 10 - x + x
Simplify
4 + x = 10
Subtract 4 from both sides
4 + x - 4 = 10 - 4
Simplify
x = 6
Answer is A. {6}
Question 6: x - (-16) = 7
Steps:
x - (-16) = 7
x - 16 = 7
Add 16 to both sides
x - 16 + 16 = 7 + 16
Simplify
x = 23
Answer is D. {23}
Question 7: -30p = -360
Steps:
-30p = -360
Divide by both sides
[tex]\frac{-30p}{-30}[/tex] = [tex]\frac{-360}{-30}[/tex]
Simplify
[tex]\frac{-30p}{-30}[/tex]
Apply the fraction rule
[tex]\frac{-30p}{-30}[/tex] = [tex]\frac{30p}{30}[/tex]
Divide the numbers
[tex]\frac{30p}{30}[/tex] = p
Simplify again
[tex]\frac{-360}{-30}[/tex] = [tex]\frac{360}{30}[/tex]
Divide the numbers
[tex]\frac{360}{30}[/tex] = 12
p = 12
Answer is B. {12}
Question 8: 14x = -252
Steps:
14x = -252
Divide both sides by 14
[tex]\frac{14x}{14}[/tex] = [tex]\frac{-252}{14}[/tex]
Simplify
[tex]\frac{14x}{14}[/tex] = x
Simplify again
[tex]\frac{-252}{14}[/tex]
Apply the fraction rule
[tex]\frac{-252}{14}[/tex] = -[tex]\frac{252}{14}[/tex]
Divide the numbers
-[tex]\frac{252}{14}[/tex] = -18
x = -18
Answer is B. {-18}
Question 9: -39 = x - 18
Solve:
-39 = x - 18
Switch sides
x - 18 = -39
Add 18 to both sides
x - 18 + 18 = -39 + 18
Simplify
x = -21
Answer is B. {-21}
Question 10: m - (-27) = -2
Steps:
m - (-27) = -2
Apply rule: For example, - (-a) = a
m + 27 = -2
Subtract 27 from both sides
m + 27 - 27 = -2 - 27
Simplify
m = -29
Answer is A. {-29}
I hope this helps you understand how to solve them next time :)
