Solve Linear Equation: 2(x-4)+6(x+2)=-18 Step-by-Step

To solve the problem $2(x-4)+6(x+2)=-18$, we follow these steps:

• Step 1: Apply the distributive property.

Expand both terms using the distributive property:

$2(x-4)$ expands to $2x - 8$ and $6(x+2)$ expands to $6x + 12$.

Thus, the equation becomes:

$2x - 8 + 6x + 12 = -18$

• Step 2: Combine like terms.

Combine $2x$ and $6x$ to get $8x$, and combine $-8$ and $12$ to get $4$.

The equation simplifies to:

$8x + 4 = -18$

• Step 3: Isolate the variable $x$.

Subtract $4$ from both sides to isolate terms with $x$:

$8x = -18 - 4$

Simplifying the right side gives:

$8x = -22$

• Step 4: Solve for $x$.

Divide both sides by $8$ to solve for $x$:

$x = \frac{-22}{8}$

Simplify $\frac{-22}{8}$ to $-\frac{11}{4}$, which is $-2\frac{3}{4}$ in mixed number form.

Therefore, the solution to the equation is $x = -2\frac{3}{4}$.