Question

1. for each expression, combine like terms, and write an equivalent expression with fewer terms.

a. $4x + 3x$

b. $3x + 5x - 1$

c. $5 + 2x + 7 + 4x$

d. $4 - 2x + 5x$

e. $10x - 5 + 3x - 2$

1. for each equation, find a value for $x$ that makes the equation true.

a. $x \div 3 = 12$

b. $2x + 3 = 20$

c. $\frac{4}{3}x = \frac{10}{3}$

d. $-4x = -24$

e. $2(x - 4) = 10$

f. $-0.5x + 1.1 = -2.9$

Explanation:

Question 7 (Combining Like Terms)

Part a: \( 4x + 3x \)

Step1: Identify like terms (both have \( x \))

\( 4x + 3x \)

Step2: Combine coefficients (\( 4 + 3 = 7 \))

\( (4 + 3)x = 7x \)

Step1: Combine like terms with \( x \) (\( 3x + 5x \))

\( 3x + 5x = (3 + 5)x = 8x \)

Step2: Include the constant term

\( 8x - 1 \)

Step1: Combine constant terms (\( 5 + 7 \))

\( 5 + 7 = 12 \)

Step2: Combine like terms with \( x \) (\( 2x + 4x \))

\( 2x + 4x = (2 + 4)x = 6x \)

Step3: Combine results

\( 12 + 6x \) (or \( 6x + 12 \))

Answer:

\( 7x \)

Part b: \( 3x + 5x - 1 \)