Solve the inequality 2x - 3 <= 5 and write the answer in interval notation.

Step-by-step solution

1. 1

   Undo the operations in reverse order. The expression $2x-3$ multiplies by $2$ and then subtracts $3$, so to isolate $x$ you undo the subtraction first and the multiplication second.

2. 2

   Add $3$ to both sides. Addition never changes the direction of an inequality:

   $2x-3+3\le 5+3\quad\Longrightarrow\quad 2x\le 8$

3. 3

   Divide both sides by $2$. The divisor is positive, so $\le$ stays $\le$:

   $x\le 4$

4. 4

   Write the interval and check the endpoint. A non-strict inequality includes its boundary, so the bracket is square:

   $(-\infty,\,4]$

   At $x=4$: $2(4)-3=5\le 5$ $\checkmark$. At $x=0$: $-3\le 5$ $\checkmark$. At $x=10$: $17\not\le 5$ $\checkmark$.