1. 6x < 2x - 8
Subtract 2x from both sides: 4x < -8
Divide by 4: x < -2
Graph: Open circle at -2, arrow to the left.
2. -3x ≥ 15
Divide by -3 (reverse inequality): x ≤ -5
Graph: Closed circle at -5, arrow to the left.
3. 2(3x + 1) > 26
Distribute: 6x + 2 > 26
Subtract 2: 6x > 24
Divide by 6: x > 4
Graph: Open circle at 4, arrow to the right.
4. x/2 - 1 ≤ 14
Add 1: x/2 ≤ 15
Multiply by 2: x ≤ 30
Graph: Closed circle at 30, arrow to the left.
5. 5x ≥ 7x - 18
Subtract 7x: -2x ≥ -18
Divide by -2 (reverse inequality): x ≤ 9
Graph: Closed circle at 9, arrow to the left.
6. (x - 3)/4 < -2
Multiply by 4: x - 3 < -8
Add 3: x < -5
Graph: Open circle at -5, arrow to the left.
7. (1/3)x + 5 ≤ -4
Subtract 5: (1/3)x ≤ -9
Multiply by 3: x ≤ -27
Graph: Closed circle at -27, arrow to the left.
8. -4x + 3x > 9
Combine like terms: -x > 9
Multiply by -1 (reverse inequality): x < -9
Graph: Open circle at -9, arrow to the left.
Parent Tip: Review the logic above to help your child master the concept of one variable inequalities worksheet.
