Question

1. $-4x + 3 \leq -17$

a) $x \geq 4$ b) $x \geq -50$
c) $x \geq 5$ d) $x \leq 4$
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d

1. solve the inequality. *

1 point

1. $10p - 4 < 196$

a) $p < 20$ b) $p > 20$
c) $p > -11$ d) $p > -32$
\bigcirc a
\bigcirc b
\bigcirc c

Explanation:

Question 4

Step1: Subtract 3 from both sides

$-4x + 3 - 3 \leq -17 - 3$
$-4x \leq -20$

Step2: Divide by -4 (reverse inequality)

$\frac{-4x}{-4} \geq \frac{-20}{-4}$
$x \geq 5$ Wait, no, wait: Wait, -20 divided by -4 is 5? Wait, no, -17 -3 is -20. Then -4x ≤ -20. Dividing both sides by -4 (inequality flips) gives x ≥ 5? Wait, no, wait the options: Option C is x ≥5, but wait let's check again. Wait, original inequality: -4x +3 ≤ -17. Subtract 3: -4x ≤ -20. Divide by -4: x ≥ 5? Wait, but option A is x ≥4. Wait, I must have miscalculated. Wait, -17 -3 is -20? Wait, -17 -3 is -20? Yes. Then -4x ≤ -20. Divide both sides by -4: x ≥ 5? Wait, but let's check with x=5: -45 +3 = -20 +3 = -17. So -17 ≤ -17, which is true. x=4: -44 +3 = -16 +3 = -13. -13 ≤ -17? No, -13 is greater than -17. So x must be ≥5. So option C. Wait, but the options: A) x≥4, B)x≥-50, C)x≥5, D)x≤4. So correct is C? Wait, no, wait my calculation: -4x +3 ≤ -17. Subtract 3: -4x ≤ -20. Divide by -4: x ≥ 5. Yes. So answer is C.

Wait, but maybe I made a mistake. Let's recheck:

-4x +3 ≤ -17
Subtract 3: -4x ≤ -20
Divide by -4 (inequality reverses): x ≥ 5. Yes. So option C.

Question 5

Step1: Add 4 to both sides

$10p -4 +4 < 196 +4$
$10p < 200$

Step2: Divide by 10

$\frac{10p}{10} < \frac{200}{10}$
$p < 20$

So the answer is A) p < 20.

Final Answers:

Question 4

Answer:

C) \( x \geq 5 \)

Question 5