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Solve the following equation for
x. Express your answer in the simplest form.

-5(-4x+3)=16 x-16

Solve the following equation for $x$ . Express your answer in the simplest form. $\newline$ $-5(-4 x+3)=16 x-16$ $\newline$

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Write and solve direct variation equations

Full solution

Q. Solve the following equation for

x

. Express your answer in the simplest form.

\newline

-5(-4 x+3)=16 x-16

\newline

Distribute and Simplify: Distribute the $-5$ across the terms inside the parentheses. $-5 \times -4x$ gives us $20x$ , and $-5 \times 3$ gives us $-15$ . So the equation becomes $20x - 15 = 16x - 16$ .
Move Terms: Move all terms containing $x$ to one side of the equation and constants to the other side. $\newline$ Subtract $16x$ from both sides to get $20x - 16x$ on the left side. $\newline$ $20x - 16x - 15 = 16x - 16x - 16$ $\newline$ This simplifies to $4x - 15 = -16$ .
Isolate Variable Term: Isolate the variable term by adding $15$ to both sides of the equation. $\newline$ $4x - 15 + 15 = -16 + 15$ $\newline$ This simplifies to $4x = -1$ .
Solve for x: Solve for x by dividing both sides by $4$ . $\newline$ $\frac{4x}{4} = \frac{-1}{4}$ $\newline$ This simplifies to $x = -\frac{1}{4}$ .

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