Question

solve the equation and check your solution.
2x - 4 = 7x + 11
x = \boxed{}

Explanation:

Step1: Subtract $2x$ from both sides

$2x - 4 - 2x = 7x + 11 - 2x$
$-4 = 5x + 11$

Step2: Subtract 11 from both sides

$-4 - 11 = 5x + 11 - 11$
$-15 = 5x$

Step3: Divide by 5 on both sides

$\frac{-15}{5} = \frac{5x}{5}$
$x = -3$

Step4: Verify the solution

Substitute $x=-3$ into original equation:
Left side: $2(-3) - 4 = -6 - 4 = -10$
Right side: $7(-3) + 11 = -21 + 11 = -10$
Both sides are equal, so the solution is valid.

Answer:

$x = -3$