Question
Simplify \( 7(3 x+5)-11 x \). Enter the answer in factored form.
Ask by Fuentes Estrada. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified and factored form of the expression is \( 5(2x + 7) \).
Solution
To simplify the expression 7(3x + 5) − 11x, follow these steps:
1. Distribute 7 to both terms inside the parentheses:
7 × 3x + 7 × 5 = 21x + 35.
2. Rewrite the expression:
21x + 35 − 11x.
3. Combine like terms by subtracting 11x from 21x:
(21x − 11x) + 35 = 10x + 35.
4. Factor out the greatest common factor, which is 5:
10x + 35 = 5(2x + 7).
Thus, the expression in factored form is 5(2x + 7).
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Simplify this solution Beyond the Answer
To simplify \( 7(3x+5)-11x \), first distribute the 7: \[ 7 \cdot 3x + 7 \cdot 5 - 11x = 21x + 35 - 11x \] Next, combine like terms: \[ (21x - 11x) + 35 = 10x + 35 \] Now, we can factor out the common factor, which is 5: \[ 10x + 35 = 5(2x + 7) \] So, the expression in factored form is: \[ 5(2x + 7) \]
