Question
What is the value of \( \frac{9 x-2}{4}+2(3+7 x) \) when \( x=4 \) ? (A) 71
Ask by Edwards Jimenez. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
When \( x=4 \), the value of \( \frac{9x-2}{4}+2(3+7x) \) is 70.5.
Solution
Substitute \( x=4 \) into the expression \( \frac{9x-2}{4}+2(3+7x) \).
Evaluate the expression by following steps:
- step0: Evaluate:
\(\frac{9x-2}{4}+2\left(3+7x\right)\)
- step1: Substitute:
\(\frac{9\times 4-2}{4}+2\left(3+7\times 4\right)\)
- step2: Multiply the numbers:
\(\frac{9\times 4-2}{4}+2\left(3+28\right)\)
- step3: Add the numbers:
\(\frac{9\times 4-2}{4}+2\times 31\)
- step4: Multiply the numbers:
\(\frac{36-2}{4}+2\times 31\)
- step5: Subtract the numbers:
\(\frac{34}{4}+2\times 31\)
- step6: Reduce the fraction:
\(\frac{17}{2}+2\times 31\)
- step7: Multiply the numbers:
\(\frac{17}{2}+62\)
- step8: Reduce fractions to a common denominator:
\(\frac{17}{2}+\frac{62\times 2}{2}\)
- step9: Transform the expression:
\(\frac{17+62\times 2}{2}\)
- step10: Multiply the numbers:
\(\frac{17+124}{2}\)
- step11: Add the numbers:
\(\frac{141}{2}\)
The value of \( \frac{9x-2}{4}+2(3+7x) \) when \( x=4 \) is \( 70.5 \).
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Simplify this solution Bonus Knowledge
First, let's substitute \( x = 4 \) into the expression: \[ \frac{9(4) - 2}{4} + 2(3 + 7(4)) \] Calculating each part step-by-step: 1. For the first term: \[ \frac{9(4) - 2}{4} = \frac{36 - 2}{4} = \frac{34}{4} = 8.5 \] 2. For the second term: \[ 2(3 + 7(4)) = 2(3 + 28) = 2(31) = 62 \] Now, combine the two results: \[ 8.5 + 62 = 70.5 \] Since none of the answer choices directly provide \( 70.5 \), the value of the expression when \( x = 4 \) is \( 70.5 \), thus the answer does not match the option given (A) 71.
