Question

1. two - step $\frac{b}{2}-20=-4$; 9. $-171 = 19v+19$; 10. $-10=\frac{1}{2}k + 3$; 11. $-17=\frac{2}{3}k-6$

Explanation:

Step1: Solve equation 8

Isolate $\frac{b}{2}$ first. Add 20 to both sides of $\frac{b}{2}-20 = - 4$.
$\frac{b}{2}-20 + 20=-4 + 20$
$\frac{b}{2}=16$
Then multiply both sides by 2 to solve for b.
$b = 16\times2=32$

Step2: Solve equation 9

Isolate the term with v. Subtract 19 from both sides of $-171 = 19v+19$.
$-171-19=19v + 19-19$
$-190 = 19v$
Then divide both sides by 19 to solve for v.
$v=\frac{-190}{19}=-10$

Step3: Solve equation 10

Isolate the term with k. Subtract 3 from both sides of $-10=\frac{1}{2}k + 3$.
$-10-3=\frac{1}{2}k+3 - 3$
$-13=\frac{1}{2}k$
Then multiply both sides by 2 to solve for k.
$k=-13\times2=-26$

Step4: Solve equation 11

Isolate the term with k. Add 6 to both sides of $-17=\frac{2}{3}k-6$.
$-17 + 6=\frac{2}{3}k-6 + 6$
$-11=\frac{2}{3}k$
Then multiply both sides by $\frac{3}{2}$ to solve for k.
$k=-11\times\frac{3}{2}=-\frac{33}{2}=-16.5$

Answer:

1. $b = 32$
2. $v=-10$
3. $k=-26$
4. $k = - 16.5$