Question

2 is the inequality true or false?
the table shows four inequalities and four values for ( x ). take turns with your partner to decide whether each value makes each inequality true, and complete the table with \true\ or \false\.

• for each decision you make, explain to your partner how you know it’s true or false.
• for each decision that your partner makes, listen carefully to their explanation. if you disagree, discuss your thinking and work to reach an agreement.

table with ( x ) values 0, 100, -100, 25 and inequalities ( x leq 25 ), ( 100 < 4x ), ( 3x > -75 ), ( 10 geq 35 - x )

Explanation:

Step1: Evaluate $x \leq 25$ for $x=0$

Substitute $x=0$: $0 \leq 25$ → True

Step2: Evaluate $x \leq 25$ for $x=-100$

Substitute $x=-100$: $-100 \leq 25$ → True

Step3: Evaluate $100 < 4x$ for $x=0$

Substitute $x=0$: $100 < 4(0) \to 100 < 0$ → False

Step4: Evaluate $100 < 4x$ for $x=100$

Substitute $x=100$: $100 < 4(100) \to 100 < 400$ → True

Step5: Evaluate $100 < 4x$ for $x=-100$

Substitute $x=-100$: $100 < 4(-100) \to 100 < -400$ → False

Step6: Evaluate $100 < 4x$ for $x=25$

Substitute $x=25$: $100 < 4(25) \to 100 < 100$ → False

Step7: Evaluate $3x > -75$ for $x=0$

Substitute $x=0$: $3(0) > -75 \to 0 > -75$ → True

Step8: Evaluate $3x > -75$ for $x=100$

Substitute $x=100$: $3(100) > -75 \to 300 > -75$ → True

Step9: Evaluate $3x > -75$ for $x=-100$

Substitute $x=-100$: $3(-100) > -75 \to -300 > -75$ → False

Step10: Evaluate $3x > -75$ for $x=25$

Substitute $x=25$: $3(25) > -75 \to 75 > -75$ → True

Step11: Evaluate $10 \geq 35 - x$ for $x=0$

Substitute $x=0$: $10 \geq 35 - 0 \to 10 \geq 35$ → False

Step12: Evaluate $10 \geq 35 - x$ for $x=100$

Substitute $x=100$: $10 \geq 35 - 100 \to 10 \geq -65$ → True

Step13: Evaluate $10 \geq 35 - x$ for $x=-100$

Substitute $x=-100$: $10 \geq 35 - (-100) \to 10 \geq 135$ → False

Step14: Evaluate $10 \geq 35 - x$ for $x=25$

Substitute $x=25$: $10 \geq 35 - 25 \to 10 \geq 10$ → True

Answer:

$x$	0	100	-100	25
$100 < 4x$	False	True	False	False
$3x > -75$	True	True	False	True
$10 \geq 35 - x$	False	True	False	True