Question

(13) $\frac{5}{2}x + 2 = 12 - \frac{5}{2}x$
(14) $-14 - 3.2y = 8.8y + 16$
(15) $-\frac{1}{5}w + 4 = \frac{3}{5}w + 24$
(16) $\frac{1}{4}u - 8 = \frac{3}{4}u$
(17) $9.7c - 13 = 7 + 9.2c$
(18) $-12 - \frac{9}{2}b = -\frac{3}{2}b - 18$
(19) $-6 + \frac{4}{7}a = \frac{3}{7}a - 11$
(20) $\frac{7}{3}y - 6 = \frac{5}{3}y + 10$
(21) $18 - 14.9x = -4.4x - 3$

Explanation:

Step1: Solve equation (13) $\frac{5}{2}x + 2 = 12 - \frac{5}{2}x$

Add $\frac{5}{2}x$ to both sides: $\frac{5}{2}x+\frac{5}{2}x + 2 = 12 - \frac{5}{2}x+\frac{5}{2}x$
Simplify: $5x + 2 = 12$
Subtract 2 from both sides: $5x + 2 - 2 = 12 - 2$
Simplify: $5x = 10$
Divide by 5: $x = \frac{10}{5} = 2$

Step2: Solve equation (14) $-14 - 3.2y = 8.8y + 16$

Add $3.2y$ to both sides: $-14 - 3.2y + 3.2y = 8.8y + 3.2y + 16$
Simplify: $-14 = 12y + 16$
Subtract 16: $-14 - 16 = 12y + 16 - 16$
Simplify: $-30 = 12y$
Divide by 12: $y = \frac{-30}{12} = -2.5$

Step3: Solve equation (15) $-\frac{1}{5}w + 4 = \frac{3}{5}w + 24$

Add $\frac{1}{5}w$ to both sides: $-\frac{1}{5}w+\frac{1}{5}w + 4 = \frac{3}{5}w+\frac{1}{5}w + 24$
Simplify: $4 = \frac{4}{5}w + 24$
Subtract 24: $4 - 24 = \frac{4}{5}w + 24 - 24$
Simplify: $-20 = \frac{4}{5}w$
Multiply by $\frac{5}{4}$: $w = -20\times\frac{5}{4} = -25$

Step4: Solve equation (16) $\frac{1}{4}u - 8 = \frac{3}{4}u$

Subtract $\frac{1}{4}u$: $\frac{1}{4}u - \frac{1}{4}u - 8 = \frac{3}{4}u - \frac{1}{4}u$
Simplify: $-8 = \frac{2}{4}u = \frac{1}{2}u$
Multiply by 2: $u = -16$

Step5: Solve equation (17) $9.7c - 13 = 7 + 9.2c$

Subtract $9.2c$: $9.7c - 9.2c - 13 = 7 + 9.2c - 9.2c$
Simplify: $0.5c - 13 = 7$
Add 13: $0.5c - 13 + 13 = 7 + 13$
Simplify: $0.5c = 20$
Divide by 0.5: $c = 40$

Step6: Solve equation (18) $-12 - \frac{9}{2}b = -\frac{3}{2}b - 18$

Add $\frac{9}{2}b$: $-12 - \frac{9}{2}b + \frac{9}{2}b = -\frac{3}{2}b + \frac{9}{2}b - 18$
Simplify: $-12 = \frac{6}{2}b - 18 = 3b - 18$
Add 18: $-12 + 18 = 3b - 18 + 18$
Simplify: $6 = 3b$
Divide by 3: $b = 2$

Step7: Solve equation (19) $-6 + \frac{4}{7}a = \frac{3}{7}a - 11$

Subtract $\frac{3}{7}a$: $-6 + \frac{4}{7}a - \frac{3}{7}a = \frac{3}{7}a - \frac{3}{7}a - 11$
Simplify: $-6 + \frac{1}{7}a = -11$
Add 6: $-6 + 6 + \frac{1}{7}a = -11 + 6$
Simplify: $\frac{1}{7}a = -5$
Multiply by 7: $a = -35$

Step8: Solve equation (20) $\frac{7}{3}y - 6 = \frac{5}{3}y + 10$

Subtract $\frac{5}{3}y$: $\frac{7}{3}y - \frac{5}{3}y - 6 = \frac{5}{3}y - \frac{5}{3}y + 10$
Simplify: $\frac{2}{3}y - 6 = 10$
Add 6: $\frac{2}{3}y - 6 + 6 = 10 + 6$
Simplify: $\frac{2}{3}y = 16$
Multiply by $\frac{3}{2}$: $y = 16\times\frac{3}{2} = 24$

Step9: Solve equation (21) $18 - 14.9x = -4.4x - 3$

Add $14.9x$: $18 - 14.9x + 14.9x = -4.4x + 14.9x - 3$
Simplify: $18 = 10.5x - 3$
Add 3: $18 + 3 = 10.5x - 3 + 3$
Simplify: $21 = 10.5x$
Divide by 10.5: $x = 2$

Answer:

(13) $x = 2$
(14) $y = -2.5$
(15) $w = -25$
(16) $u = -16$
(17) $c = 40$
(18) $b = 2$
(19) $a = -35$
(20) $y = 24$
(21) $x = 2$