Question

8: identify each number that makes the inequality true.
4x + 7 < 43
(handwritten steps: subtract 7 from both sides, divide by 4, result x < 9? wait, original handwritten has some errors, but the problem is to identify numbers from options a:12, b:9, c:6 (partially obscured), d:3, e: -...
10: what is not a solution to:
-3p - 12 ≤ -36
(handwritten start: +12 +12)

Explanation:

Step1: Solve the inequality \(4x + 7 < 43\)

Subtract 7 from both sides: \(4x + 7 - 7 < 43 - 7\), which simplifies to \(4x < 36\).

Step2: Divide both sides by 4

\(\frac{4x}{4} < \frac{36}{4}\), so \(x < 9\).

Step3: Check each option

• A: \(12\): \(12 < 9\)? No.
• B: \(9\): \(9 < 9\)? No.
• C: \(6\): \(6 < 9\)? Yes.
• D: \(3\): \(3 < 9\)? Yes.
• E: (Assuming it's a negative number, negative numbers are less than 9, so yes.)

For the numbers that make the inequality true, we look for \(x < 9\). So 6 (C), 3 (D), and any negative number (E) are solutions. If we consider the options given (A:12, B:9, C:6, D:3), the numbers that make it true are C. 6, D. 3. (If E is a negative, it's also a solution, but from visible options, C and D.)

(For question 10, let's solve \(-3p - 12 \leq -36\))

Step1: Add 12 to both sides

\(-3p - 12 + 12 \leq -36 + 12\), so \(-3p \leq -24\).

Step2: Divide by -3 (reverse inequality)

\(\frac{-3p}{-3} \geq \frac{-24}{-3}\), so \(p \geq 8\).
Now, find what is NOT a solution (values less than 8).

Answer:

For question 8 (numbers making \(4x + 7 < 43\) true): C. 6, D. 3 (and E if negative).
For question 10 (what is NOT a solution to \(-3p - 12 \leq -36\)): Any number less than 8 (e.g., 7, 0, -5, etc.). If options were given, we'd check, but based on solving, \(p \geq 8\), so numbers like 7, 5, etc., are not solutions.