Question

Solving compound inequalities
X+8>=7 and 8x-2>=6

Answer 1

x ≥ 1

Explanation:

The solution set must satisfy both of the compound inequalities.

First inequality

x +8 ≥ 7

x ≥ -1 . . . . . subtract 1 from both sides

Second inequality

8x -2 ≥ 6

8x ≥ 8 . . . . . . add 2 to both sides

x ≥ 1 . . . . . . . . divide both sides by 8

Solution set

The solution set of the compound inequality will be the set of values of x that satisfy both. This will be the region of overlap between the two intervals ...

• -1 ≤ x < ∞
• 1 ≤ x < ∞

That region of overlap will be the interval ...

1 ≤ x < ∞ . . . . . solution to the compound intequality