Question

solve each equation for the designated variable.

1. solve for m:

y = mx + 5

1. solve for b:

p = 2a + 3b + c

1. solve for c:

r=\frac{c + d}{2}

1. solve for s:

a=\frac{pi r^{2}cdot s}{360}

1. solve for y:

ax + by = c

1. solve for b:

x = 2(a + 2b + 3c)

Explanation:

Step1: Isolate mx term

Subtract 5 from both sides of $y = mx+5$.
$y - 5=mx$

Step2: Solve for m

Divide both sides by x (assuming $x
eq0$).
$m=\frac{y - 5}{x}$

Step3: For $P = 2a+3b + c$, isolate 3b term

Subtract 2a and c from both sides.
$3b=P - 2a - c$

Step4: Solve for b

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

Step5: For $R=\frac{c + d}{2}$, isolate c + d term

Multiply both sides by 2.
$2R=c + d$

Step6: Solve for c

Subtract d from both sides.
$c=2R - d$

Step7: For $A=\frac{\pi r^{2}\cdot S}{360}$, isolate $\pi r^{2}\cdot S$ term

Multiply both sides by 360.
$360A=\pi r^{2}\cdot S$

Step8: Solve for S

Divide both sides by $\pi r^{2}$ (assuming $\pi r^{2}
eq0$).
$S=\frac{360A}{\pi r^{2}}$

Step9: For $Ax+By = C$, isolate By term

Subtract Ax from both sides.
$By=C - Ax$

Step10: Solve for y

Divide both sides by B (assuming $B
eq0$).
$y=\frac{C - Ax}{B}$

Step11: For $x = 2(a + 2b+3c)$, first expand the right - hand side

$x = 2a+4b + 6c$

Step12: Isolate 4b term

Subtract 2a and 6c from both sides.
$4b=x - 2a - 6c$

Step13: Solve for b

Divide both sides by 4.
$b=\frac{x - 2a - 6c}{4}$

Answer:

1. $m=\frac{y - 5}{x}$
2. $b=\frac{P - 2a - c}{3}$
3. $c=2R - d$
4. $S=\frac{360A}{\pi r^{2}}$
5. $y=\frac{C - Ax}{B}$
6. $b=\frac{x - 2a - 6c}{4}$