Question

directions: rearrange each equation below and solve for the given variable.
1 solve for t: ( d = rt )
2 solve for t: ( p = irt )
3 solve for b: ( y = mx + b )
4 solve for y: ( ax + by = c )
5 solve for w: ( p = 2ell + 2w )
6 solve for h: ( a = \frac{1}{2}bh )
7 solve for c: ( f = \frac{9}{5}c + 32 )
8 solve for h: ( a = \frac{1}{2}h(b + c) )
9 solve for x: ( y = \frac{1}{x} + b )
10 solve for y: ( \frac{4x + y}{m} = q )
11 solve for m: ( 2y = \frac{m}{4}(6a - 5b) )
12 solve for s: ( \frac{s}{ve} - 0 = l )

Explanation:

1. Solve for $t$: $d=rt$

Step1: Divide both sides by $r$

$\frac{d}{r} = \frac{rt}{r}$

Step2: Simplify to isolate $t$

$t = \frac{d}{r}$

2. Solve for $t$: $P=Irt$

Step1: Divide both sides by $Ir$

$\frac{P}{Ir} = \frac{Irt}{Ir}$

Step2: Simplify to isolate $t$

$t = \frac{P}{Ir}$

3. Solve for $b$: $y=mx+b$

Step1: Subtract $mx$ from both sides

$y - mx = mx + b - mx$

Step2: Simplify to isolate $b$

$b = y - mx$

4. Solve for $y$: $Ax+By=C$

Step1: Subtract $Ax$ from both sides

$By = C - Ax$

Step2: Divide both sides by $B$

$y = \frac{C - Ax}{B}$

5. Solve for $w$: $P=2l+2w$

Step1: Subtract $2l$ from both sides

$P - 2l = 2w$

Step2: Divide both sides by 2

$w = \frac{P - 2l}{2}$

6. Solve for $h$: $A=\frac{1}{2}bh$

Step1: Multiply both sides by 2

$2A = bh$

Step2: Divide both sides by $b$

$h = \frac{2A}{b}$

7. Solve for $C$: $F=\frac{9}{5}C+32$

Step1: Subtract 32 from both sides

$F - 32 = \frac{9}{5}C$

Step2: Multiply by $\frac{5}{9}$

$C = \frac{5}{9}(F - 32)$

8. Solve for $h$: $A=\frac{1}{2}h(b+c)$

Step1: Multiply both sides by 2

$2A = h(b+c)$

Step2: Divide by $(b+c)$

$h = \frac{2A}{b+c}$

9. Solve for $x$: $y=\frac{1}{x}+b$

Step1: Subtract $b$ from both sides

$y - b = \frac{1}{x}$

Step2: Take reciprocal of both sides

$x = \frac{1}{y - b}$

10. Solve for $y$: $\frac{4x+y}{m}=q$

Step1: Multiply both sides by $m$

$4x + y = qm$

Step2: Subtract $4x$ from both sides

$y = qm - 4x$

11. Solve for $m$: $2y=\frac{m}{4}(6a-5b)$

Step1: Multiply both sides by 4

$8y = m(6a - 5b)$

Step2: Divide by $(6a-5b)$

$m = \frac{8y}{6a - 5b}$

12. Solve for $s$: $\frac{s}{VE}-0=L$

Step1: Simplify the left side

$\frac{s}{VE} = L$

Step2: Multiply by $VE$

$s = LVE$

Answer:

1. $\boldsymbol{t = \frac{d}{r}}$
2. $\boldsymbol{t = \frac{P}{Ir}}$
3. $\boldsymbol{b = y - mx}$
4. $\boldsymbol{y = \frac{C - Ax}{B}}$
5. $\boldsymbol{w = \frac{P - 2l}{2}}$
6. $\boldsymbol{h = \frac{2A}{b}}$
7. $\boldsymbol{C = \frac{5}{9}(F - 32)}$
8. $\boldsymbol{h = \frac{2A}{b+c}}$
9. $\boldsymbol{x = \frac{1}{y - b}}$
10. $\boldsymbol{y = qm - 4x}$
11. $\boldsymbol{m = \frac{8y}{6a - 5b}}$
12. $\boldsymbol{s = LVE}$