Question

solve the inequality and graph the solution
-3x + 5 _< 8 on a number line
do it step by step

Answer 1

Solve -3x + 5 ≤ 8 step by step:

1. Start with the inequality:
-3x + 5 ≤ 8

2. Subtract 5 from both sides:
-3x ≤ 3

3. Divide both sides by -3. Because you divide by a negative number, reverse the inequality sign:
x ≥ -1

Solution: x ≥ -1. In interval notation: [-1, ∞).

Quick checks:
- x = 0: -3(0)+5 = 5 ≤ 8 (true)
- x = -2: -3(-2)+5 = 11 ≤ 8 (false)

Graph on a number line (● = closed dot at -1, arrow to the right shows all numbers ≥ -1):

... -4 -3 -2 -1 0 1 2 ...
●────────────────────►