Question

1. solve for b. y = mx + bz
2. solve for a. c = 1/2(b + a)
3. solve for h. a = πr²h
4. solve for z. y = kz/x
5. solve for w. r = 2w - t
6. solve for a. h = 3a + b²
7. solve for c. k = (4ac - b)/2a

Explanation:

Step1: Isolate the variable b in $y = mx + bz$

Subtract $mx$ from both sides.
$y - mx=bz$

Step2: Solve for b

Divide both sides by z (assuming $z
eq0$).
$b=\frac{y - mx}{z}$

Step3: Isolate the variable a in $c=\frac{1}{2}(b + a)$

Multiply both sides by 2.
$2c=b + a$

Step4: Solve for a

Subtract b from both sides.
$a = 2c - b$

Step5: Isolate the variable h in $A=\pi r^{2}h$

Divide both sides by $\pi r^{2}$ (assuming $r
eq0$).
$h=\frac{A}{\pi r^{2}}$

Step6: Isolate the variable z in $y=\frac{kz}{x}$

Multiply both sides by x.
$yx = kz$

Step7: Solve for z

Divide both sides by k (assuming $k
eq0$).
$z=\frac{yx}{k}$

Step8: Isolate the variable w in $r = 2w - t$

Add t to both sides.
$r + t=2w$

Step9: Solve for w

Divide both sides by 2.
$w=\frac{r + t}{2}$

Step10: Isolate the variable a in $h = 3a + b^{2}$

Subtract $b^{2}$ from both sides.
$h - b^{2}=3a$

Step11: Solve for a

Divide both sides by 3.
$a=\frac{h - b^{2}}{3}$

Step12: Isolate the variable c in $k=\frac{4ac - b}{2a}$

Multiply both sides by 2a.
$2ak=4ac - b$

Step13: Move terms involving c to one - side

$2ak + b=4ac$

Step14: Solve for c

Divide both sides by 4a (assuming $a
eq0$).
$c=\frac{2ak + b}{4a}$

Answer:

1. $b=\frac{y - mx}{z}$
2. $a = 2c - b$
3. $h=\frac{A}{\pi r^{2}}$
4. $z=\frac{yx}{k}$
5. $w=\frac{r + t}{2}$
6. $a=\frac{h - b^{2}}{3}$
7. $c=\frac{2ak + b}{4a}$