Question

1. rearrange each of the following equations to isolate for x.

a) $y = mx + b$
b) $a = \frac{bx}{c}$
c) $ax + b = c - y$
d) $a = b - cx$
e) $b + y = cx - a$
f) $a + 2x = cy$
g) $a + 2x - b = c - y$
h) $\frac{x}{a} + b - y = -c$

Explanation:

Step1: Isolate mx term

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

Step2: Solve for x

Divide both sides by $m$.
$x = \frac{y - b}{m}$

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Step1: Eliminate denominator c

Multiply both sides by $c$.
$ac = bx$

Step2: Solve for x

Divide both sides by $b$.
$x = \frac{ac}{b}$

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Step1: Isolate ax term

Subtract $b$ from both sides.
$ax = c - y - b$

Step2: Solve for x

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

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Step1: Isolate cx term

Rearrange to move $cx$ left and $a$ right.
$cx = b - a$

Step2: Solve for x

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

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Step1: Isolate cx term

Add $a$ to both sides.
$b + y + a = cx$

Step2: Solve for x

Divide both sides by $c$.
$x = \frac{a + b + y}{c}$

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Step1: Isolate 2x term

Subtract $a$ from both sides.
$2x = cy - a$

Step2: Solve for x

Divide both sides by 2.
$x = \frac{cy - a}{2}$

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Step1: Isolate 2x term

Combine constants and rearrange.
$2x = c - y - a + b$

Step2: Solve for x

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

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Step1: Isolate $\frac{x}{a}$ term

Rearrange constants to the right.
$\frac{x}{a} = -c - b + y$

Step2: Solve for x

Multiply both sides by $a$.
$x = a(y - b - c)$

Answer:

a) $x = \frac{y - b}{m}$
b) $x = \frac{ac}{b}$
c) $x = \frac{c - y - b}{a}$
d) $x = \frac{b - a}{c}$
e) $x = \frac{a + b + y}{c}$
f) $x = \frac{cy - a}{2}$
g) $x = \frac{c - y - a + b}{2}$
h) $x = a(y - b - c)$