Answer
$x = 1$
Work Step by Step
We use the definition that $|x|=a \longrightarrow x=-a \quad \text{or} \quad x=a$ to obtain:
$$2x + 8 = 3x + 7\quad \text{or} \quad2x + 8 = - (3x + 7)$$
Solve the first equation first. Subtract $8$ from each side to isolate the constants to one side:
$$2x = 3x - 1$$
We now subtract $3x$ from each side to isolate the variable to one side:
$$-x = -1$$
Divide each side by $-1$ to isolate the $x$:
$$x = 1$$
Let's solv
Solve the other equation. Use distributive property on the right side of the equation to obtain:
$$2x + 8 = - 3x - 7$$
Subtract $8$ from each side of the equation to isolate the constants to one side:
$$2x = - 3x - 15$$
Add $3x$ to each side to isolate the variable to one side of the equation:
$$5x = -15$$
Divide both sides of the equation by $5$ to isolate the $x$:
$$x = -3$$
Check for extraneous solutions. Plug $x = 1$ into the original equation.
$|2(1) + 8| = 3(1) + 7$
Multiply out:
$|2 + 8| = 3 + 7$
Add constants on each side of the equation:
$|10| = 10$
This statement is true; therefore, 1 is a solution of this equation.
Substitute $-3$ for $x$:
$|2(-3) + 8| = 3(-3) + 7$
Multiply out:
$|-6 + 8| = -9 + 7$
Add constants on each side of the equation:
$|2| = -2$
This statement is false; therefore, $-3$ is not a solution of this equation.
