Question

question 6: solve the following equations
(a) ( 3x + 3 = x + 8 )
(b) ( 9x + 10 = 7x + 39 )
(c) ( 3x + 1 = 7x - 11 )
(d) ( x + 4 = 13 - x )
(e) ( 16x + 3 = 6x + 24 )
(f) ( 9x + 12 = 6x + 14 )
(g) ( 7x + 24 = 12x - 12 )
(h) ( 2x + 9 = 48 - 6x )
(i) ( 34 - 12x = 28x - 36 )

Explanation:

(a) Step1: Isolate x terms

$3x - x = 8 - 3$

(a) Step2: Simplify and solve

$2x = 5 \implies x = \frac{5}{2}$

(b) Step1: Isolate x terms

$9x - 7x = 39 - 10$

(b) Step2: Simplify and solve

$2x = 29 \implies x = \frac{29}{2}$

(c) Step1: Isolate x terms

$3x - 7x = -17 - 1$

(c) Step2: Simplify and solve

$-4x = -18 \implies x = \frac{9}{2}$

(d) Step1: Isolate x terms

$x + x = 13 - 4$

(d) Step2: Simplify and solve

$2x = 9 \implies x = \frac{9}{2}$

(e) Step1: Isolate x terms

$16x - 6x = 24 - 3$

(e) Step2: Simplify and solve

$10x = 21 \implies x = \frac{21}{10}$

(f) Step1: Isolate x terms

$9x - 6x = 14 - 12$

(f) Step2: Simplify and solve

$3x = 2 \implies x = \frac{2}{3}$

(g) Step1: Isolate x terms

$7x - 12x = -12 - 24$

(g) Step2: Simplify and solve

$-5x = -36 \implies x = \frac{36}{5}$

(h) Step1: Isolate x terms

$2x + 6x = 48 - 9$

(h) Step2: Simplify and solve

$8x = 39 \implies x = \frac{39}{8}$

(i) Step1: Isolate x terms

$-12x - 28x = -36 - 34$

(i) Step2: Simplify and solve

$-40x = -70 \implies x = \frac{7}{4}$

Answer:

(a) $x = \frac{5}{2}$
(b) $x = \frac{29}{2}$
(c) $x = \frac{9}{2}$
(d) $x = \frac{9}{2}$
(e) $x = \frac{21}{10}$
(f) $x = \frac{2}{3}$
(g) $x = \frac{36}{5}$
(h) $x = \frac{39}{8}$
(i) $x = \frac{7}{4}$