Question

1. $3a - 6a + 2 = 8a + 20 - 5a$
2. $8 - 6m = 4m + 48$
3. $4y = 38 - \frac{1}{2}(4y + 16)$

Explanation:

Problem 5:

Step1: Combine like terms on both sides

Left: $3a - 6a + 2 = -3a + 2$
Right: $8a - 5a + 20 = 3a + 20$
Equation becomes: $-3a + 2 = 3a + 20$

Step2: Move $a$ terms to left side

Subtract $3a$ from both sides:
$-3a - 3a + 2 = 20$
$-6a + 2 = 20$

Step3: Move constants to right side

Subtract 2 from both sides:
$-6a = 20 - 2$
$-6a = 18$

Step4: Solve for $a$

Divide by $-6$:
$a = \frac{18}{-6}$

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Problem 7:

Step1: Move $m$ terms to left side

Add $6m$ to both sides:
$8 = 4m + 6m + 48$
$8 = 10m + 48$

Step2: Move constants to left side

Subtract 48 from both sides:
$8 - 48 = 10m$
$-40 = 10m$

Step3: Solve for $m$

Divide by 10:
$m = \frac{-40}{10}$

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Problem 9:

Step1: Distribute the fraction on right side

$4y = 38 - \frac{1}{2}(4y) - \frac{1}{2}(16)$
$4y = 38 - 2y - 8$

Step2: Combine constants on right side

$4y = 30 - 2y$

Step3: Move $y$ terms to left side

Add $2y$ to both sides:
$4y + 2y = 30$
$6y = 30$

Step4: Solve for $y$

Divide by 6:
$y = \frac{30}{6}$

Answer:

Problem 5: $a = -3$
Problem 7: $m = -4$
Problem 9: $y = 5$