Question
Solve. \( 6-5(3 x-4)=-34 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is \( x=\square \). (Simplify your answer.) B. The solution is all real numbers. C. There is no solution.
Ask by Patel Gray. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is \( x = 4 \).
Solution
To solve the equation 6 - 5(3x - 4) = -34, start by distributing the -5 across the parentheses:
6 - 15x + 20 = -34
Combine like terms (6 + 20):
26 - 15x = -34
Next, subtract 26 from both sides to isolate the term with x:
-15x = -34 - 26
-15x = -60
Now, divide both sides by -15:
x = (-60) / (-15)
x = 4
Therefore, the correct choice is:
A. The solution is x = 4.
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Simplify this solution Beyond the Answer
To solve the equation \( 6 - 5(3x - 4) = -34 \), let's follow the steps: First, distribute \( -5 \) across \( (3x - 4) \): \[ 6 - 15x + 20 = -34 \] Combine like terms on the left side: \[ 26 - 15x = -34 \] Next, subtract 26 from both sides: \[ -15x = -34 - 26 \] \[ -15x = -60 \] Now, divide by -15: \[ x = \frac{-60}{-15} = 4 \] So the solution is: A. The solution is \( x=4 \).
