Question

1. solve for a. c = a + b
2. solve for h. y = \frac{h}{x}
3. solve for w. y = bx + aw
4. solve for z. a = \frac{bz}{c}
5. solve for h. v = s^{2}h
6. solve for r. c = 2\pi r
7. solve for l. v = lwh

Explanation:

Step1: Isolate a in c = a + b

Subtract b from both sides: $c - b=a + b - b$

Step2: Simplify the right - hand side

$a=c - b$

Step3: Isolate h in $y=\frac{h}{x}$

Multiply both sides by x: $y\times x=\frac{h}{x}\times x$

Step4: Simplify the right - hand side

$h = xy$

Step5: Isolate w in $y=bx + aw$

Subtract bx from both sides: $y - bx=bx + aw - bx$

Step6: Simplify the right - hand side

$y - bx=aw$

Step7: Solve for w

Divide both sides by a (assuming $a
eq0$): $w=\frac{y - bx}{a}$

Step8: Isolate z in $a=\frac{bz}{c}$

Multiply both sides by c: $a\times c=\frac{bz}{c}\times c$

Step9: Simplify the right - hand side

$ac = bz$

Step10: Solve for z

Divide both sides by b (assuming $b
eq0$): $z=\frac{ac}{b}$

Step11: Isolate h in $V = s^{2}h$

Divide both sides by $s^{2}$ (assuming $s
eq0$): $h=\frac{V}{s^{2}}$

Step12: Isolate r in $C = 2\pi r$

Divide both sides by $2\pi$: $r=\frac{C}{2\pi}$

Step13: Isolate l in $V = lwh$

Divide both sides by wh (assuming $wh
eq0$): $l=\frac{V}{wh}$

Answer:

1. $a=c - b$
2. $h = xy$
3. $w=\frac{y - bx}{a}$
4. $z=\frac{ac}{b}$
5. $h=\frac{V}{s^{2}}$
6. $r=\frac{C}{2\pi}$
7. $l=\frac{V}{wh}$