Question

solving equations ii

1. solve each equation. be sure to show all necessary steps.

$39 - 12w = 7 - 16w$
$63 - x = 2x + 3$
$12r - 1.8 = 13r + 1.8$
$-15w - 40 = 23 - 8w$

1. solve each equation. then perform a ls/rs check.

$-x - 1 = x - 21$
$3n + 46 = 1 + 8n$

Explanation:

For 1. Solve each equation:

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Equation 1: $39 - 12w = 7 - 16w$

Step1: Isolate $w$ terms to left

Add $16w$ to both sides:
$39 - 12w + 16w = 7 - 16w + 16w$
$39 + 4w = 7$

Step2: Isolate constant terms to right

Subtract 39 from both sides:
$39 + 4w - 39 = 7 - 39$
$4w = -32$

Step3: Solve for $w$

Divide both sides by 4:
$\frac{4w}{4} = \frac{-32}{4}$

Step1: Isolate $x$ terms to right

Add $x$ to both sides:
$63 - x + x = 2x + 3 + x$
$63 = 3x + 3$

Step2: Isolate constant terms to left

Subtract 3 from both sides:
$63 - 3 = 3x + 3 - 3$
$60 = 3x$

Step3: Solve for $x$

Divide both sides by 3:
$\frac{60}{3} = \frac{3x}{3}$

Step1: Isolate $r$ terms to right

Subtract $12r$ from both sides:
$12r - 1.8 - 12r = 13r + 1.8 - 12r$
$-1.8 = r + 1.8$

Step2: Solve for $r$

Subtract 1.8 from both sides:
$-1.8 - 1.8 = r + 1.8 - 1.8$

Answer:

$w = -8$

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Equation 2: $63 - x = 2x + 3$