Question

1. $9(p + 3) = 5p - 1$
2. $11n - 19 = 4(2n + 5)$
3. $4(4c - 3) = 2(5c + 18)$
4. $-2(3r - 14) = 4(13 - r)$
5. $-\frac{5}{2}(8y - 2) = 5(10 - y)$
6. $-3(2w + 5) + 7w = 5(w - 11)$

Explanation:

Problem 7:

Step1: Expand left side

$9p + 27 = 5p - 1$

Step2: Isolate $p$ terms

$9p - 5p = -1 - 27$

Step3: Simplify both sides

$4p = -28$

Step4: Solve for $p$

$p = \frac{-28}{4} = -7$

Problem 8:

Step1: Expand right side

$11n - 19 = 8n + 20$

Step2: Isolate $n$ terms

$11n - 8n = 20 + 19$

Step3: Simplify both sides

$3n = 39$

Step4: Solve for $n$

$n = \frac{39}{3} = 13$

Problem 9:

Step1: Expand both sides

$16c - 12 = 10c + 36$

Step2: Isolate $c$ terms

$16c - 10c = 36 + 12$

Step3: Simplify both sides

$6c = 48$

Step4: Solve for $c$

$c = \frac{48}{6} = 8$

Problem 10:

Step1: Expand both sides

$-6r + 28 = 52 - 4r$

Step2: Isolate $r$ terms

$-6r + 4r = 52 - 28$

Step3: Simplify both sides

$-2r = 24$

Step4: Solve for $r$

$r = \frac{24}{-2} = -12$

Problem 11:

Step1: Expand both sides

$-20y + 5 = 50 - 5y$

Step2: Isolate $y$ terms

$-20y + 5y = 50 - 5$

Step3: Simplify both sides

$-15y = 45$

Step4: Solve for $y$

$y = \frac{45}{-15} = -3$

Problem 12:

Step1: Expand and simplify left side

$-6w - 15 + 7w = 5(w - 11)$
$w - 15 = 5w - 55$

Step2: Isolate $w$ terms

$w - 5w = -55 + 15$

Step3: Simplify both sides

$-4w = -40$

Step4: Solve for $w$

$w = \frac{-40}{-4} = 10$

Answer:

1. $p = -7$
2. $n = 13$
3. $c = 8$
4. $r = -12$
5. $y = -3$
6. $w = 10$