Here are the step-by-step solutions for each inequality on the worksheet.
1. $7w \leq 42$
*
Goal: Isolate $w$.
*
Step: Divide both sides by 7. Since 7 is positive, the inequality sign stays the same.
*
Calculation: $w \leq 42 / 7$
*
Result: $w \leq 6$
2. $\frac{k}{4} \leq -4$
*
Goal: Isolate $k$.
*
Step: Multiply both sides by 4. Since 4 is positive, the inequality sign stays the same.
*
Calculation: $k \leq -4 \times 4$
*
Result: $k \leq -16$
3. $-5 > \frac{p}{8}$
*
Goal: Isolate $p$.
*
Step: Multiply both sides by 8. Since 8 is positive, the inequality sign stays the same.
*
Calculation: $-5 \times 8 > p$
*
Result: $-40 > p$ (or written as $p < -40$)
4. $15 < r + 14$
*
Goal: Isolate $r$.
*
Step: Subtract 14 from both sides.
*
Calculation: $15 - 14 < r$
*
Result: $1 < r$ (or written as $r > 1$)
5. $3k \geq -24$
*
Goal: Isolate $k$.
*
Step: Divide both sides by 3. Since 3 is positive, the inequality sign stays the same.
*
Calculation: $k \geq -24 / 3$
*
Result: $k \geq -8$
6. $-6 \geq \frac{m}{4}$
*
Goal: Isolate $m$.
*
Step: Multiply both sides by 4. Since 4 is positive, the inequality sign stays the same.
*
Calculation: $-6 \times 4 \geq m$
*
Result: $-24 \geq m$ (or written as $m \leq -24$)
7. $\frac{t}{6} < -3$
*
Goal: Isolate $t$.
*
Step: Multiply both sides by 6. Since 6 is positive, the inequality sign stays the same.
*
Calculation: $t < -3 \times 6$
*
Result: $t < -18$
8. $-5 < \frac{1}{3}t$
*
Goal: Isolate $t$.
*
Step: Multiply both sides by 3 to remove the fraction. Since 3 is positive, the inequality sign stays the same.
*
Calculation: $-5 \times 3 < t$
*
Result: $-15 < t$ (or written as $t > -15$)
9. $-6 < s - 11$
*
Goal: Isolate $s$.
*
Step: Add 11 to both sides.
*
Calculation: $-6 + 11 < s$
*
Result: $5 < s$ (or written as $s > 5$)
10. $x + 14 \geq -5$
*
Goal: Isolate $x$.
*
Step: Subtract 14 from both sides.
*
Calculation: $x \geq -5 - 14$
*
Result: $x \geq -19$
Final Answer:
1. $w \leq 6$
2. $k \leq -16$
3. $p < -40$
4. $r > 1$
5. $k \geq -8$
6. $m \leq -24$
7. $t < -18$
8. $t > -15$
9. $s > 5$
10. $x \geq -19$
Parent Tip: Review the logic above to help your child master the concept of basic inequalities worksheet.
