Question

1. what does x equal in the equation below?

4x - 2 = 10

1. solve for x: 3x + 2x = 20

a. 4 b. 5 c. 10 d. 20

1. given the equation 3(x + 4) = 33, what is the value of x?

a. 7 b. 15 c. \frac{29}{3} d. \frac{37}{3}

Explanation:

Question 1

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the equation \( 4x - 2 = 10 \). This gives us \( 4x - 2 + 2 = 10 + 2 \), which simplifies to \( 4x = 12 \).

Step2: Divide by 4

Next, we divide both sides of the equation \( 4x = 12 \) by 4 to solve for \( x \). So, \( \frac{4x}{4} = \frac{12}{4} \), which simplifies to \( x = 3 \).

Step1: Combine like terms

First, we combine the like terms on the left side of the equation \( 3x + 2x = 20 \). Combining \( 3x \) and \( 2x \) gives us \( 5x = 20 \).

Step2: Divide by 5

Then, we divide both sides of the equation \( 5x = 20 \) by 5. This gives us \( \frac{5x}{5} = \frac{20}{5} \), so \( x = 4 \)? Wait, no, wait. Wait, \( 3x + 2x = 5x \), so \( 5x = 20 \), then \( x = 20 \div 5 = 4 \)? But the options have B as 5. Wait, no, I must have made a mistake. Wait, \( 3x + 2x = 5x \), so \( 5x = 20 \), so \( x = 4 \)? But the options are A. 4, B. 5, C. 10, D. 20. Wait, maybe I miscalculated. Wait, \( 3x + 2x = 5x \), so \( 5x = 20 \), so \( x = 4 \), which is option A? But the handwritten note says \( 6x = 20 \), which is wrong. So the correct answer is A. 4? Wait, no, wait, \( 3x + 2x = 5x \), so \( 5x = 20 \), so \( x = 4 \). So the correct option is A. 4.

Step1: Divide by 3

First, we divide both sides of the equation \( 3(x + 4) = 33 \) by 3. This gives us \( \frac{3(x + 4)}{3} = \frac{33}{3} \), which simplifies to \( x + 4 = 11 \).

Step2: Subtract 4

Next, we subtract 4 from both sides of the equation \( x + 4 = 11 \). This gives us \( x + 4 - 4 = 11 - 4 \), so \( x = 7 \).

Answer:

\( x = 3 \)

Question 2