Questions: Solve -4(x+2)+6=-1(x+8) for x x=

Transcript text: Solve $-4(x+2)+6=-1(x+8)$ for $x$ \[ x= \]

Solution

Step 1: Distribute the Constants

First, distribute the constants on both sides of the equation:

\[ -4(x+2) + 6 = -1(x+8) \]

Distribute $-4$ on the left side:

\[ -4x - 8 + 6 \]

Distribute $-1$ on the right side:

\[ -x - 8 \]

Step 2: Simplify Both Sides

Simplify the expressions on both sides of the equation:

Left side:

\[ -4x - 8 + 6 = -4x - 2 \]

Right side:

\[ -x - 8 \]

The equation now is:

\[ -4x - 2 = -x - 8 \]

Step 3: Solve for $x$

To solve for $x$, first add $4x$ to both sides:

\[ -2 = 3x - 8 \]

Next, add $8$ to both sides:

\[ 6 = 3x \]

Finally, divide both sides by $3$:

\[ x = 2 \]

\[ \boxed{x = 2} \]

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