Question

Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6

Answer 1

`\{a` ∈
`R\ -21 \le a \le \infty \}` --- set builder

`[-21,\infty)` --- interval notation

Explanation:

Given

`-3a - 15 \le -2a + 6`

Required

Solve

Collect like terms

`-3a + 2a \le 15 + 6`

`-a \le 21`

Divide by -1

`a \ge - 21`

Rewrite as:

`-21 \le a`

Using set builder

`\{a` ∈
`R\ -21 \le a \le \infty \}`

Using interval notation, we have:

`[-21,\infty)`