Here are the step-by-step solutions for each inequality on the worksheet.
1) $\frac{x}{2} + 3 > 9$
* Subtract 3 from both sides: $\frac{x}{2} > 6$
* Multiply both sides by 2: $x > 12$
*
Graph: Open circle at 12, arrow pointing to the right.
2) $4x + 5 \leq 13$
* Subtract 5 from both sides: $4x \leq 8$
* Divide both sides by 4: $x \leq 2$
*
Graph: Closed (filled) circle at 2, arrow pointing to the left.
3) $7x - 19 < 16$
* Add 19 to both sides: $7x < 35$
* Divide both sides by 7: $x < 5$
*
Graph: Open circle at 5, arrow pointing to the left.
4) $\frac{x - 4}{5} \geq 2$
* Multiply both sides by 5: $x - 4 \geq 10$
* Add 4 to both sides: $x \geq 14$
*
Graph: Closed (filled) circle at 14, arrow pointing to the right.
5) $9 + 3x > 12$
* Subtract 9 from both sides: $3x > 3$
* Divide both sides by 3: $x > 1$
*
Graph: Open circle at 1, arrow pointing to the right.
6) $3x - 4 \leq 5$
* Add 4 to both sides: $3x \leq 9$
* Divide both sides by 3: $x \leq 3$
*
Graph: Closed (filled) circle at 3, arrow pointing to the left.
7) $\frac{x}{8} + 1 < 3$
* Subtract 1 from both sides: $\frac{x}{8} < 2$
* Multiply both sides by 8: $x < 16$
*
Graph: Open circle at 16, arrow pointing to the left.
8) $2x + 5 \geq 19$
* Subtract 5 from both sides: $2x \geq 14$
* Divide both sides by 2: $x \geq 7$
*
Graph: Closed (filled) circle at 7, arrow pointing to the right.
Final Answer:
1) x > 12
2) x ≤ 2
3) x < 5
4) x ≥ 14
5) x > 1
6) x ≤ 3
7) x < 16
8) x ≥ 7
Parent Tip: Review the logic above to help your child master the concept of solve two step inequalities worksheet.
