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Solving Multi-Step Equations

Solving Multi-Step Equations 1.7 - Solution

a
Start by multiplying $4$ into the parentheses. We can then solve for $x$ using inverse operations.
$4(x - 3) + 2 = 10$
$4 \cdot x - 4 \cdot 3 + 2 = 10$
$4x - 12 + 2 = 10$
$4x - 10 = 10$
$4x = 20$
$x = 5$
b
First, multiply $3$ to the terms inside parentheses. Then, gather all the variables on one side and the constants on the other.
$2x + 7 = \text{-} 4 + 3(8 + 5x)$
$2x + 7 = \text{-} 4 + 3 \cdot 8 + 3 \cdot 5x$
$2x + 7 = \text{-} 4 + 24 + 15x$
$2x + 7 = 20 + 15x$
$7 = 20 + 13x$
$\text{-} 13 = 13x$
$13x=\text{-} 13$
$x = \text{-} 1$
c
On the left-hand side we can start by distributing $2.$ Then we remove the parentheses on the left-hand side and change signs on the terms inside.
$5 + 2(\text{-} 7 + x) = \text{-} 6 - (\text{-} x + 8)$
$5 + 2(\text{-}7) + 2 \cdot x = \text{-} 6 - (\text{-} x + 8)$
$5 -14 + 2x = \text{-} 6 - (\text{-} x + 8)$
$5 -14 + 2x = \text{-} 6 +x - 8$
$\text{-} 9 + 2x = x - 14$
$2x = x - 5$
$x= \text{-} 5$