Here are the step-by-step solutions for each inequality.
1) $5x - 39 > x$
* Subtract $x$ from both sides: $4x - 39 > 0$
* Add 39 to both sides: $4x > 39$
* Divide by 4: $x > 9.75$ (or $x > \frac{39}{4}$)
2) $3x + 15 \leq 14$
* Subtract 15 from both sides: $3x \leq -1$
* Divide by 3: $x \leq -\frac{1}{3}$
3) $19 - 2x < 43$
* Subtract 19 from both sides: $-2x < 24$
* Divide by -2.
Remember: When you divide by a negative number, flip the inequality sign.
* Result: $x > -12$
4) $2x + 18 \geq 5x - 17$
* Subtract $2x$ from both sides: $18 \geq 3x - 17$
* Add 17 to both sides: $35 \geq 3x$
* Divide by 3: $\frac{35}{3} \geq x$
* Rewrite with $x$ first: $x \leq \frac{35}{3}$ (or $x \leq 11.66...$)
5) $3x - 48 < 32 - 5x$
* Add $5x$ to both sides: $8x - 48 < 32$
* Add 48 to both sides: $8x < 80$
* Divide by 8: $x < 10$
6) $4x + 13 \leq 7x + 38$
* Subtract $4x$ from both sides: $13 \leq 3x + 38$
* Subtract 38 from both sides: $-25 \leq 3x$
* Divide by 3: $-\frac{25}{3} \leq x$
* Rewrite with $x$ first: $x \geq -\frac{25}{3}$ (or $x \geq -8.33...$)
7) $10x - 16 < 8(x - 4)$
* Distribute the 8 on the right side: $10x - 16 < 8x - 32$
* Subtract $8x$ from both sides: $2x - 16 < -32$
* Add 16 to both sides: $2x < -16$
* Divide by 2: $x < -8$
8) $3(x + 5) < 7x - 5$
* Distribute the 3 on the left side: $3x + 15 < 7x - 5$
* Subtract $3x$ from both sides: $15 < 4x - 5$
* Add 5 to both sides: $20 < 4x$
* Divide by 4: $5 < x$
* Rewrite with $x$ first: $x > 5$
Final Answer:
1) $x > 9.75$
2) $x \leq -\frac{1}{3}$
3) $x > -12$
4) $x \leq \frac{35}{3}$
5) $x < 10$
6) $x \geq -\frac{25}{3}$
7) $x < -8$
8) $x > 5$
Parent Tip: Review the logic above to help your child master the concept of solving multi step inequalities worksheet.
