Question

question 1: (i) $\frac{x}{4}=1.6$ (j) $\frac{x}{2.5}=8$ (k) $\frac{x}{4}=-3$ (l) $\frac{x}{6}=-12$ 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):

Isolate $\frac{x}{4}$ first. Subtract 1 from both sides of $\frac{x}{4}+1 = 9$.
$\frac{x}{4}=9 - 1=8$
Then multiply both sides by 4 to solve for $x$.
$x = 8\times4=32$

Question 2(b):

Isolate $\frac{x}{2}$ first. Add 5 to both sides of $\frac{x}{2}-5 = 9$.
$\frac{x}{2}=9 + 5=14$
Then multiply both sides by 2 to solve for $x$.
$x=14\times2 = 28$

Question 2(c):

Isolate $\frac{w}{5}$ first. Subtract 2 from both sides of $\frac{w}{5}+2 = 3$.
$\frac{w}{5}=3 - 2=1$
Then multiply both sides by 5 to solve for $w$.
$w=1\times5 = 5$

Question 2(d):

Isolate $\frac{x}{8}$ first. Add 7 to both sides of $\frac{x}{8}-7 = 2$.
$\frac{x}{8}=2 + 7=9$
Then multiply both sides by 8 to solve for $x$.
$x=9\times8 = 72$

Question 2(e):

Isolate $\frac{m}{3}$ first. Add 4 to both sides of $\frac{m}{3}-4 = 0$.
$\frac{m}{3}=0 + 4=4$
Then multiply both sides by 3 to solve for $m$.
$m=4\times3 = 12$

Question 2(f):

Isolate $\frac{x}{6}$ first. Subtract 7 from both sides of $\frac{x}{6}+7 = 2$.
$\frac{x}{6}=2 - 7=-5$
Then multiply both sides by 6 to solve for $x$.
$x=-5\times6=-30$

Question 2(g):

Isolate $\frac{k}{4}$ first. Subtract 5 from both sides of $\frac{k}{4}+5=-6$.
$\frac{k}{4}=-6 - 5=-11$
Then multiply both sides by 4 to solve for $k$.
$k=-11\times4=-44$

Question 2(h):

Isolate $\frac{x}{6}$ first. Add 2 to both sides of $\frac{x}{6}-2=-8$.
$\frac{x}{6}=-8 + 2=-6$
Then multiply both sides by 6 to solve for $x$.
$x=-6\times6=-36$

Question 3(a):

Multiply both sides of $\frac{x + 1}{2}=3$ by 2.
$x + 1=3\times2=6$
Then subtract 1 from both sides to solve for $x$.
$x=6 - 1=5$

Question 3(b):

Multiply both sides of $\frac{w - 4}{3}=2$ by 3.
$w - 4=2\times3=6$
Then add 4 to both sides to solve for $w$.
$w=6 + 4=10$

Question 3(c):

Multiply both sides of $\frac{x - 2}{7}=6$ by 7.
$x - 2=6\times7=42$
Then add 2 to both sides to solve for $x$.
$x=42+2 = 44$

Question 3(d):

Multiply both sides of $\frac{w + 9}{4}=8$ by 4.
$w + 9=8\times4=32$
Then subtract 9 from both sides to solve for $w$.
$w=32 - 9=23$

Question 3(e):

Multiply both sides of $\frac{w - 25}{3}=-7$ by 3.
$w - 25=-7\times3=-21$
Then add 25 to both sides to solve for $w$.
$w=-21 + 25=4$

Question 3(f):

Multiply both sides of $\frac{x + 2}{4}=-1$ by 4.
$x + 2=-1\times4=-4$
Then subtract 2 from both sides to solve for $x$.
$x=-4 - 2=-6$

Question 3(g):

Multiply both sides of $\frac{w + 20}{8}=-2$ by 8.
$w + 20=-2\times8=-16$
Then subtract 20 from both sides to solve for $w$.
$w=-16 - 20=-36$

Question 3(h):

Multiply both sides of $\frac{x - 9}{4}=-2$ by 4.
$x - 9=-2\times4=-8$
Then add 9 to both sides to solve for $x$.
$x=-8 + 9=1$

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) $x = 1$