Question

1. which value of w makes ( w - 2 = 3(6 - w) ) true?

a. 2
b. 3
c. 4
d. 5

Explanation:

Problem 5

Step1: Test x=2.4

$2.4 + 7.4 = 9.8
eq 10$

Step2: Test x=2.6

$2.6 + 7.4 = 10$

Step3: Test x=3.6

$3.6 + 7.4 = 11
eq 10$

Problem 6

Step1: Test y=$\frac{2}{7}$

$\frac{3}{5} \times \frac{2}{7} = \frac{6}{35}$

Step2: Test y=2

$\frac{3}{5} \times 2 = \frac{6}{5}
eq \frac{6}{35}$

Step3: Test y=7

$\frac{3}{5} \times 7 = \frac{21}{5}
eq \frac{6}{35}$

Problem 7

Step1: Test x=8

$\frac{1}{4}(2\times8 - 8) = \frac{1}{4}(16-8) = \frac{1}{4}\times8 = 2
eq 3$

Step2: Test x=12

$\frac{1}{4}(2\times12 - 8) = \frac{1}{4}(24-8) = \frac{1}{4}\times16 = 4
eq 3$

Step3: Test x=16

$\frac{1}{4}(2\times16 - 8) = \frac{1}{4}(32-8) = \frac{1}{4}\times24 = 6
eq 3$
Note: No given number satisfies this equation

Problem 8

Step1: Expand right-hand side

$w - 2 = 18 - 3w$

Step2: Isolate w terms

$w + 3w = 18 + 2$

Step3: Simplify and solve

$4w = 20 \implies w = \frac{20}{4} = 5$
Verify: $5-2=3$, $3(6-5)=3$, so $3=3$

Answer:

1. 2.6
2. $\frac{2}{7}$
3. None of the given numbers
4. D. 5