In order to solve the inequality 5(x - 3) - 6(x - 2) ≤ 8 follow these steps:
1. Distribute the products on the left side and get rid of the parenthesis:
5(x - 3) - 6(x - 2) ≤ 8
5x - 5×3 - 6x + 6×2 ≤ 8
5x - 15 - 6x + 12 ≤ 8
2. Combine like terms on the left:
5x - 15 - 6x + 12 ≤ 8
5x - 6x - 15 + 12 ≤ 8
-x - 3 ≤ 8
3. Add 3 on both sides:
-x - 3 ≤ 8
-x - 3 + 3 ≤ 8 + 3
-x ≤ 11
4. Multiply both sides and invert the inequality symbol:
x ≥ -11
Then the solution for the given inequality is all the numbers that are greater or equal to 11. We can graph this solution on a number line like this: