To solve the inequality 5x - 1_1 - 2x ≤ 8 + x/3, we can follow these steps:
1. Combine like terms on both sides of the inequality. On the left side, combine 5x and -2x to get 3x. On the right side, simplify 8 + x/3 to (24 + x)/3.
The inequality becomes:
3x - 1_1 ≤ (24 + x)/3
2. Multiply both sides of the inequality by 3 to eliminate the fraction.
3 * (3x - 1_1) ≤ 3 * (24 + x)/3
Simplifying, we get:
9x - 9_3 ≤ 24 + x
3. Distribute the 3 on the left side.
9x - 27_3 ≤ 24 + x
4. Combine like terms on both sides of the inequality. On the left side, combine 9x and x to get 10x. On the right side, simplify 24 + x to 24 + x.
The inequality becomes:
10x - 27 ≤ 24 + x
5. Subtract x from both sides to isolate the variable.
10x - x - 27 ≤ 24 + x - x
Simplifying, we get:
9x - 27 ≤ 24
6. Add 27 to both sides to further isolate the variable.
9x - 27 + 27 ≤ 24 + 27
Simplifying, we get:
9x ≤ 51
7. Divide both sides by 9 to solve for x.
(9x)/9 ≤ 51/9
Simplifying, we get:
x ≤ 5.67
Therefore, the solution to the inequality 5x - 1_1 - 2x ≤ 8 + x/3 is x ≤ 5.67.
