Question

question 2: solve the following equations (a) $\frac{x}{4}+1 = 9$ (b) $\frac{x}{2}-5 = 9$ (c) $\frac{w}{5}+2 = 3$ (d) $\frac{x}{8}-7 = 2$ (e) $\frac{m}{3}-4 = 0$ (f) $\frac{x}{6}+7 = 2$ (g) $\frac{k}{4}+5=-6$ (h) $\frac{x}{6}-2=-8$ question 3: solve the following equations (a) $\frac{x + 1}{2}=3$ (b) $\frac{w - 4}{3}=2$ (c) $\frac{x - 2}{7}=6$ (d) $\frac{w + 9}{4}=8$ (e) $\frac{w - 25}{3}=-7$ (f) $\frac{x + 2}{4}=-1$ (g) $\frac{w + 20}{8}=-2$ (h) $\frac{x - 9}{4}=-2$

Explanation:

Question 2:

(a)

Step1: Isolate the fraction

Subtract 1 from both sides of $\frac{x}{4}+1 = 9$.
$\frac{x}{4}=9 - 1=8$

Step2: Solve for x

Multiply both sides by 4.
$x = 8\times4=32$

(b)

Step1: Isolate the fraction

Add 5 to both sides of $\frac{x}{2}-5 = 9$.
$\frac{x}{2}=9 + 5=14$

Step2: Solve for x

Multiply both sides by 2.
$x=14\times2 = 28$

(c)

Step1: Isolate the fraction

Subtract 2 from both sides of $\frac{w}{5}+2 = 3$.
$\frac{w}{5}=3 - 2=1$

Step2: Solve for w

Multiply both sides by 5.
$w=1\times5 = 5$

(d)

Step1: Isolate the fraction

Add 7 to both sides of $\frac{x}{8}-7 = 2$.
$\frac{x}{8}=2 + 7=9$

Step2: Solve for x

Multiply both sides by 8.
$x=9\times8 = 72$

(e)

Step1: Isolate the fraction

Add 4 to both sides of $\frac{m}{3}-4 = 0$.
$\frac{m}{3}=0 + 4=4$

Step2: Solve for m

Multiply both sides by 3.
$m=4\times3 = 12$

(f)

Step1: Isolate the fraction

Subtract 7 from both sides of $\frac{x}{6}+7 = 2$.
$\frac{x}{6}=2 - 7=-5$

Step2: Solve for x

Multiply both sides by 6.
$x=-5\times6=-30$

(g)

Step1: Isolate the fraction

Subtract 5 from both sides of $\frac{k}{4}+5=-6$.
$\frac{k}{4}=-6 - 5=-11$

Step2: Solve for k

Multiply both sides by 4.
$k=-11\times4=-44$

(h)

Step1: Isolate the fraction

Add 2 to both sides of $\frac{x}{6}-2=-8$.
$\frac{x}{6}=-8 + 2=-6$

Step2: Solve for x

Multiply both sides by 6.
$x=-6\times6=-36$

Question 3:

(a)

Step1: Multiply both sides by 2

Given $\frac{x + 1}{2}=3$, we get $x + 1=3\times2=6$.

Step2: Solve for x

Subtract 1 from both sides.
$x=6 - 1=5$

(b)

Step1: Multiply both sides by 3

Given $\frac{w - 4}{3}=2$, we get $w - 4=2\times3 = 6$.

Step2: Solve for w

Add 4 to both sides.
$w=6+4 = 10$

(c)

Step1: Multiply both sides by 7

Given $\frac{x - 2}{7}=6$, we get $x - 2=6\times7 = 42$.

Step2: Solve for x

Add 2 to both sides.
$x=42 + 2=44$

(d)

Step1: Multiply both sides by 4

Given $\frac{w + 9}{4}=8$, we get $w + 9=8\times4 = 32$.

Step2: Solve for w

Subtract 9 from both sides.
$w=32-9 = 23$

(e)

Step1: Multiply both sides by 3

Given $\frac{w - 25}{3}=-7$, we get $w - 25=-7\times3=-21$.

Step2: Solve for w

Add 25 to both sides.
$w=-21 + 25 = 4$

(f)

Step1: Multiply both sides by 4

Given $\frac{x + 2}{4}=-1$, we get $x + 2=-1\times4=-4$.

Step2: Solve for x

Subtract 2 from both sides.
$x=-4 - 2=-6$

(g)

Step1: Multiply both sides by 8

Given $\frac{w + 20}{8}=-2$, we get $w + 20=-2\times8=-16$.

Step2: Solve for w

Subtract 20 from both sides.
$w=-16-20=-36$

(h)

Step1: Multiply both sides by 4

Given $\frac{x - 9}{4}=-2$, we get $x - 9=-2\times4=-8$.

Step2: Solve for x

Add 9 to both sides.
$x=-8 + 9=1$

Answer:

Question 2:
(a) $x = 32$
(b) $x = 28$
(c) $w = 5$
(d) $x = 72$
(e) $m = 12$
(f) $x=-30$
(g) $k=-44$
(h) $x=-36$
Question 3:
(a) $x = 5$
(b) $w = 10$
(c) $x = 44$
(d) $w = 23$
(e) $w = 4$
(f) $x=-6$
(g) $w=-36$
(h) $x = 1$