Question

1. $8x^3 - 6x^3 + 4 = 132$

a. $x = -4$
b. $x = \pm 4$
c. $x = 3$
d. $x = 4$

1. from the given bank of statement following equations in the correct blank provided.

a. $5 - x = 12$
bank:
a) add 5 to both sides.
b) subtract 5 from both sides.
c) multiply both sides by 5.
d) divide both sides by 5.
e) add 1 to both sides.
f) subtract 1 from both sides.
g) divide both sides by 1.
h) divide both sides by -1.

Explanation:

Problem 1: Solve \( 8x^3 - 6x^3 + 4 = 132 \) and choose the correct option.

Step 1: Combine like terms

First, combine the \( x^3 \) terms: \( 8x^3 - 6x^3 = 2x^3 \). So the equation becomes \( 2x^3 + 4 = 132 \).

Step 2: Subtract 4 from both sides

Subtract 4 from each side: \( 2x^3 + 4 - 4 = 132 - 4 \), which simplifies to \( 2x^3 = 128 \).

Step 3: Divide by 2

Divide both sides by 2: \( \frac{2x^3}{2} = \frac{128}{2} \), so \( x^3 = 64 \).

Step 4: Take the cube root

Take the cube root of both sides: \( x = \sqrt[3]{64} = 4 \).

To solve \( 5 - x = 12 \), we can first subtract 5 from both sides to get \( -x = 12 - 5 \), or we can also divide both sides by -1 at the end. But let's analyze the steps:

1. Start with \( 5 - x = 12 \).
2. Subtract 5 from both sides: \( 5 - x - 5 = 12 - 5 \) → \( -x = 7 \).
3. Then divide both sides by -1: \( x = -7 \). But from the bank, the first step (subtract 5) is option B, and if we consider the final step (divide by -1) is option H. Wait, maybe the question is about the first step? Wait, the problem says "from the given bank of statements, following equations in the correct blank provided" (maybe typo, but let's check the equation \( 5 - x = 12 \)).

Wait, let's re-express the equation: \( 5 - x = 12 \) can be written as \( -x + 5 = 12 \). To isolate the term with \( x \), we can subtract 5 (option B) or we can also multiply both sides by -1, but the bank has "Subtract 5 from both sides" (B) and "Divide both sides by -1" (H). Wait, maybe the intended first step is subtract 5. Let's check:

If we subtract 5 from both sides: \( 5 - x - 5 = 12 - 5 \) → \( -x = 7 \), then divide by -1 (H) to get \( x = -7 \). But maybe the question is about the first operation. Alternatively, let's see the options:

Wait, the equation is \( 5 - x = 12 \). Let's solve it step by step:

1. Subtract 5 from both sides (option B): \( 5 - x - 5 = 12 - 5 \) → \( -x = 7 \).
2. Then divide both sides by -1 (option H): \( x = -7 \).

But maybe the question is asking for the first operation. So the first operation is subtract 5 from both sides (option B), and then divide by -1 (option H). But let's check the bank options:

Bank options: A) Add 5, B) Subtract 5, C) Multiply by 5, D) Divide by 5, E) Add 1, F) Subtract 1, G) Divide by 1, H) Divide by -1.

So to solve \( 5 - x = 12 \):

• Step 1: Subtract 5 from both sides (B) to get \( -x = 7 \).
• Step 2: Divide both sides by -1 (H) to get \( x = -7 \).

But maybe the question is about the first operation. So the answer for the first step is B (Subtract 5 from both sides) and then H (Divide both sides by -1). But let's confirm.

Wait, the equation is \( 5 - x = 12 \). Let's rearrange:

\( -x = 12 - 5 \) (subtract 5) → \( -x = 7 \) → \( x = -7 \) (divide by -1). So the operations are B and H. But maybe the question is asking for the first operation. So the answer for the first step is B.

To solve \( 5 - x = 12 \), the first step is to subtract 5 from both sides (option B) to isolate the term with \( x \), leading to \( -x = 7 \). Then, dividing by -1 (option H) gives \( x = -7 \). If the question asks for the first operation, the answer is B. If it allows multiple steps, B and H are involved.

Answer:

d. \( x = 4 \)

Problem 4a: Solve \( 5 - x = 12 \) and choose the correct operation from the bank.