Question

6-51. solve each of the following equations for the indicated variable. show all of your steps. homework help a. $y = 2x - 5$ for $x$ b. $p = -aw + 9$ for $w$ c. $2m - 6 = 4n + 4$ for $m$ d. $bx - y = -2y$ for $y$

Explanation:

Step1: Isolate term with $x$

Add 5 to both sides:
$y + 5 = 2x$

Step2: Solve for $x$

Divide by 2:
$x = \frac{y + 5}{2}$

Step1: Isolate term with $w$

Subtract 9 from both sides:
$p - 9 = -aw$

Step2: Solve for $w$

Divide by $-a$:
$w = \frac{p - 9}{-a} = \frac{9 - p}{a}$

Step1: Isolate term with $m$

Add 6 to both sides:
$2m = 4n + 4 + 6$
Simplify right side:
$2m = 4n + 10$

Step2: Solve for $m$

Divide by 2:
$m = 2n + 5$

Step1: Isolate terms with $y$

Add $y$ to both sides:
$bx - y + y = -2y + y$
Simplify:
$bx = -y$

Step2: Solve for $y$

Multiply by $-1$:
$y = bx$

Answer:

a. $x = \frac{y + 5}{2}$
b. $w = \frac{p - 9}{-a}$ or $w = \frac{9 - p}{a}$
c. $m = 2n + 5$
d. $y = bx$