To solve the inequality, we will first solve each part separately.
1. Solve 2(x-3) > -6:
Distribute the 2: 2x - 6 > -6
Add 6 to both sides: 2x > 0
Divide by 2: x > 0
2. Solve 2(x-3) ≤ 13:
Distribute the 2: 2x - 6 ≤ 13
Add 6 to both sides: 2x ≤ 19
Divide by 2: x ≤ 9.5
So the solution set is x > 0 and x ≤ 9.5.
To graph the solution set, we will represent both inequalities on a number line:
(0 _______[___________) 9.5
x > 0 x ≤ 9.5
The open circle at 0 represents that x is greater than 0, and the filled circle at 9.5 represents that x is less than or equal to 9.5. Shade the region between these two points.
In interval notation, the solution set is (0, 9.5].
Solve the inequality. Graph the solution set and write it in interval notation.
-6<2(x-3)≤13
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