Solve the equation 5x - 4 = 2x + 11.

Step-by-step solution

1. 1

   Move the smaller variable term across. Subtract $2x$ from both sides:

   $5x-2x-4=11\quad\Longrightarrow\quad 3x-4=11$

2. 2

   Move the constant across. Add $4$ to both sides:

   $3x=11+4=15$

3. 3

   Divide by $3$.

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

4. 4

   Check both sides. With $x=5$:

   $\text{left}=5(5)-4=21,\qquad\text{right}=2(5)+11=21$

   Equal, so $x=5$ $\checkmark$. Because the coefficients of $x$ differ ($5\ne 2$), the equation was guaranteed to have exactly one solution — equal coefficients would have signalled either no solution or infinitely many.