Question

solving inequalities puzzle maze
directions: start with box number one. solve the equation and move in the direction of that answer until you get to the correct extended response! work your problems out on the back.
$x>24$
$x>8$
$17x<187$
$x\leq11$
$x>125$
$x\geq0$
$x\leq11$
$<16$
$x+3>6$
$x>117$
$x>15$
$+6\leq8$
$12 + 4x\geq28$
$x<7$
$6x-12<30$
$x>7$
$3x+13>34$
$7(x - 29)\leq20$
$x\leq7$
$14x-100<14.0$
$x<7.0$
$9x-54>27$
on the back: write a real world situation represented and graph it.
on the back: write a real world two-step inequality word problem, solve and graph it.
on the back: write a paragraph containing how you solve real world two-step inequalities.

Explanation:

Step1: Solve $3x > 24$

Divide both sides by 3:
$\frac{3x}{3} > \frac{24}{3}$
$x > 8$

Step2: Solve $17x < 187$

Divide both sides by 17:
$\frac{17x}{17} < \frac{187}{17}$
$x < 11$

Step3: Solve $\frac{x}{3} + 3 > 6$

Subtract 3 from both sides:
$\frac{x}{3} + 3 - 3 > 6 - 3$
$\frac{x}{3} > 3$
Multiply by 3:
$x > 9$

Step4: Solve $x + 6 \leq 8$

Subtract 6 from both sides:
$x + 6 - 6 \leq 8 - 6$
$x \leq 2$

Step5: Solve $12 + 4x \geq 28$

Subtract 12 from both sides:
$12 + 4x - 12 \geq 28 - 12$
$4x \geq 16$
Divide by 4:
$\frac{4x}{4} \geq \frac{16}{4}$
$x \geq 4$

Step6: Solve $6x - 12 < 30$

Add 12 to both sides:
$6x - 12 + 12 < 30 + 12$
$6x < 42$
Divide by 6:
$\frac{6x}{6} < \frac{42}{6}$
$x < 7$

Step7: Solve $3x + 13 > 34$

Subtract 13 from both sides:
$3x + 13 - 13 > 34 - 13$
$3x > 21$
Divide by 3:
$\frac{3x}{3} > \frac{21}{3}$
$x > 7$

Step8: Solve $7(x - 29) \leq 20$

Expand left side:
$7x - 203 \leq 20$
Add 203 to both sides:
$7x - 203 + 203 \leq 20 + 203$
$7x \leq 223$
Divide by 7:
$x \leq \frac{223}{7} \approx 31.86$

Step9: Solve $14x - 100 < 14.0$

Add 100 to both sides:
$14x - 100 + 100 < 14 + 100$
$14x < 114$
Divide by 14:
$x < \frac{114}{14} \approx 8.14$

Step10: Solve $9x - 54 > 27$

Add 54 to both sides:
$9x - 54 + 54 > 27 + 54$
$9x > 81$
Divide by 9:
$\frac{9x}{9} > \frac{81}{9}$
$x > 9$

Maze Path (Start at Box 1: $3x>24$):

1. Box1 solution: $x>8$ → move to $x>8$
2. Next connected box: $17x<187$, solution $x<11$ → move to $x<11$
3. Next connected box: $\frac{x}{3}+3>6$, solution $x>9$ → move to $x>9$ (matches $x>15$ is incorrect, correct path follows $x>9$ to next valid inequality)
4. Next valid connected box: $3x+13>34$, solution $x>7$ → move to $x>7$
5. Next connected box: $6x-12<30$, solution $x<7$ → move to $x<7$
6. Next connected box: $12+4x\geq28$, solution $x\geq4$ → move to $x\geq4$
7. Next connected box: $7(x-29)\leq20$, solution $x\leq31.86$ → move to $x\leq7$
8. Next connected box: $14x-100<14.0$, solution $x<8.14$ → move to $x<7.0$
9. Next connected box: $9x-54>27$, solution $x>9$ → ends at the extended response box: "On the back: Write a paragraph containing how you solve real world two-step inequalities."

Answer:

Solved Inequalities:

1. $3x>24$: $x>8$
2. $17x<187$: $x<11$
3. $\frac{x}{3}+3>6$: $x>9$
4. $x+6\leq8$: $x\leq2$
5. $12+4x\geq28$: $x\geq4$
6. $6x-12<30$: $x<7$
7. $3x+13>34$: $x>7$
8. $7(x-29)\leq20$: $x\leq\frac{223}{7}\approx31.86$
9. $14x-100<14.0$: $x<\frac{57}{7}\approx8.14$
10. $9x-54>27$: $x>9$

Maze End Point:

On the back: Write a paragraph containing how you solve real world two-step inequalities.