Solve for X in -2(3x+2)+1=3(x+8): Linear Equation Practice

To effectively solve the equation $-2(3x+2)+1=3(x+8)$, we'll break down each step systematically:

• Step 1: Distribute the constants $-2$ and $3$ to the terms within the parentheses on each side of the equation.
• Step 2: Simplify by combining like terms on each side.
• Step 3: Isolate the $x$ term by performing the appropriate arithmetic operations.
• Step 4: Solve for $x$.

Step 1:

Distribute $-2$ in $-2(3x + 2)$:

$-2 \times 3x = -6x$ and $-2 \times 2 = -4$.

Thus, the left side becomes $-6x - 4 + 1$.

Distribute $3$ in $3(x + 8)$:

$3 \times x = 3x$ and $3 \times 8 = 24$.

So, the right side becomes $3x + 24$.

Step 2:

Simplify both sides:

Left side: $-6x - 4 + 1 = -6x - 3$

Right side: $3x + 24$

So the equation becomes:

$-6x - 3 = 3x + 24$

Step 3:

To isolate $x$, add $6x$ to both sides:

$-3 = 9x + 24$

Step 4:

Subtract $24$ from both sides:

$-3 - 24 = 9x$

$-27 = 9x$

Divide both sides by $9$ to solve for $x$:

$x = \frac{-27}{9}$

$x = -3$

Therefore, the solution to the equation is $x = -3$.