Question

identify each number that makes the quality true.
$4x + 7 < 43$
(handwritten steps: -7 on both sides, then divide by 4, result $x < 9$? wait, original calculation: 43 -7=36, 36/4=9, so $x < 9$? wait the handwritten has 4x < 36? wait the ocr text: then options a:12, b:9, c:6, d:3, e:-12
then another question: what is not a solution to:
$-3p - 12 \leq -36$
(handwritten +12 on both sides)

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

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

Step3: Check each option

• Option A: \(12\). Since \(12

less 9\), \(12\) is not a solution.

• Option B: \(9\). Since \(9

less 9\) (it's equal), \(9\) is not a solution. Wait, but let's re - check the inequality solving. Wait, original inequality is \(4x + 7<43\). \(4x<36\), \(x < 9\). So values less than 9 are solutions.

• Option C: \(6\). \(6<9\), so it is a solution.
• Option D: \(3\). \(3 < 9\), so it is a solution.
• Option E: \(- 12\). \(-12<9\), so it is a solution.

Wait, maybe the question is "What is NOT a solution". So we need to find the number that does not satisfy \(x < 9\). So \(12\) (A) and \(9\) (B) do not satisfy \(x < 9\). But let's check the calculation again.

Wait, \(4x+7 < 43\)
Subtract 7: \(4x<36\)
Divide by 4: \(x < 9\). So numbers less than 9 are solutions. So 12 (A) and 9 (B) are not solutions. But maybe the original problem's first part is to identify numbers that make the inequality true (i.e., solutions), and then the second part (the "NOT" part) is for another inequality. But for the first inequality \(4x + 7<43\) (solving gives \(x < 9\)):

• A: 12: \(12\) is not less than 9, so not a solution.
• B: 9: 9 is not less than 9, so not a solution.
• C: 6: 6 < 9, so solution.
• D: 3: 3 < 9, so solution.
• E: - 12: - 12 < 9, so solution.

If we assume the question is about the first inequality (identify numbers that make the inequality true), then the solutions are C, D, E. But if it's "what is NOT a solution", then A and B. But let's check the hand - written work. The hand - written work has \(4x + 7<43\), subtract 7: \(4x<36\), divide by 4: \(x < 9\). So numbers less than 9 are solutions. So non - solutions are 9 and 12.

But maybe the question is from the first part "Identify each number that makes the inequality true" (i.e., find solutions). So the solutions are C (6), D (3), E (- 12).

Answer:

If the question is to find numbers that make \(4x + 7<43\) true (solutions), the answers are C. 6, D. 3, E. - 12. If it's to find non - solutions, the answers are A. 12, B. 9.