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

Question

Accepted Answer

### Part a
# Explanation:
## Step1: Identify like terms (both have $x$)
$4x$ and $3x$ are like terms.
## Step2: Combine coefficients: $4 + 3 = 7$
$4x + 3x=(4 + 3)x = 7x$
# Answer: $7x$

### Part b
# Explanation:
## Step1: Identify like terms with $x$
$3x$ and $5x$ are like terms.
## Step2: Combine $3x + 5x=(3 + 5)x = 8x$
Now the expression is $8x-1$ (since $-1$ has no like terms to combine with).
# Answer: $8x - 1$

### Part c
# Explanation:
## Step1: Group like terms (constants and terms with $x$)
Constants: $5$ and $7$; Terms with $x$: $2x$ and $4x$
## Step2: Combine constants: $5 + 7 = 12$
## Step3: Combine terms with $x$: $2x+4x=(2 + 4)x = 6x$
## Step4: Combine results: $12 + 6x$ (or $6x + 12$)
# Answer: $6x + 12$ (or $12 + 6x$)

### Part d
# Explanation:
## Step1: Identify like terms with $x$
$-2x$ and $5x$ are like terms.
## Step2: Combine $-2x+5x=(-2 + 5)x = 3x$
Now the expression is $4 + 3x$ (or $3x + 4$)
# Answer: $3x + 4$ (or $4 + 3x$)

### Part e
# Explanation:
## Step1: Group like terms (terms with $x$ and constants)
Terms with $x$: $10x$ and $3x$; Constants: $-5$ and $-2$
## Step2: Combine terms with $x$: $10x+3x=(10 + 3)x = 13x$
## Step3: Combine constants: $-5-2=-7$
## Step4: Combine results: $13x-7$
# Answer: $13x - 7$

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QUESTION IMAGE

Question

Explanation:

Part a

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

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

Step1: Identify like terms with \(x\)

Step2: Combine \(3x + 5x=(3 + 5)x = 8x\)

Step1: Group like terms (constants and terms with \(x\))

Step2: Combine constants: \(5 + 7 = 12\)

Step3: Combine terms with \(x\): \(2x+4x=(2 + 4)x = 6x\)

Step4: Combine results: \(12 + 6x\) (or \(6x + 12\))

Answer:

Part b