PROBLEM SOLVING WITH MULTI STEP EQUATIONS QUICK CHECK ANSWERS HERE |

Question

A. 12(m + 5) = 150
B. 5(m + 12) = 150
C. m + 12 (5) = 150
D. 12m + 5 = 150

Question 2: Solve -2(4 - n) = 24
A. -16
B. 16
C. 8
D. -8
Question 3: One-quarter of the difference of a number and 3 is 2. find the number.
A. 3 and 1/2
B. 11
C. 20
D. 5/4
Question 4: Solve 2/3(x - 6) = 14
A. 27
B. -15
C. 15
D. -27
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Answer 1

Sure! Let's solve each of the problems step by step.

Question 1: Solve the equations for m

A. \( 12(m + 5) = 150 \)
Solution:
\( m + 5 = \frac{150}{12} \)
\( m + 5 = 12.5 \)
\( m = 12.5 - 5 = 7.5 \)

B. \( 5(m + 12) = 150 \)
Solution:
\( m + 12 = \frac{150}{5} \)
\( m + 12 = 30 \)
\( m = 30 - 12 = 18 \)

C. \( m + 12(5) = 150 \)
Solution:
\( m + 60 = 150 \)
\( m = 150 - 60 = 90 \)

D. \( 12m + 5 = 150 \)
Solution:
\( 12m = 150 - 5 \)
\( 12m = 145 \)
\( m = \frac{145}{12} \approx 12.08 \)

Question 2: Solve -2(4 - n) = 24

Solution:
-2(4 - n) = 24
\( 4 - n = -12 \)
\( -n = -12 - 4 \)
\( -n = -16 \)
\( n = 16 \)
Correct answer: B. 16

Question 3: One-quarter of the difference of a number and 3 is 2.

Let the number be x.
\( \frac{1}{4}(x - 3) = 2 \)
Multiply both sides by 4:
\( x - 3 = 8 \)
\( x = 11 \)
Correct answer: B. 11

Question 4: Solve \(\frac{2}{3}(x - 6) = 14\)

Solution:
Multiply both sides by \(\frac{3}{2}\):
\( x - 6 = \frac{14 \times 3}{2} \)
\( x - 6 = 21 \)
\( x = 21 + 6 = 27 \)
Correct answer: A. 27

To summarize the correct answers:

1. Individually solved (not a one single answer)
2. B. 16
3. B. 11
4. A. 27