Question
Question Solve the following equation for \( x \). \[ -12+7 x-5 x=4-3 x+2 \] Give your answer as an improper fraction, if necessary.
Ask by Kirk Montgomery. in the United States
Feb 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = \frac{18}{5} \)
Solution
Solve the equation \( -12+7x-5x=4-3x+2 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(-12+7x-5x=4-3x+2\)
- step1: Subtract the terms:
\(-12+2x=6-3x\)
- step2: Move the expression to the left side:
\(2x+3x=6+12\)
- step3: Add and subtract:
\(5x=6+12\)
- step4: Add and subtract:
\(5x=18\)
- step5: Divide both sides:
\(\frac{5x}{5}=\frac{18}{5}\)
- step6: Divide the numbers:
\(x=\frac{18}{5}\)
The solution to the equation \( -12+7x-5x=4-3x+2 \) is \( x = \frac{18}{5} \) or \( x = 3.6 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To solve the equation \(-12 + 7x - 5x = 4 - 3x + 2\), we first simplify both sides of the equation: Combine like terms on the left: \[ -12 + (7x - 5x) = -12 + 2x \] Combine like terms on the right: \[ 4 + 2 = 6 - 3x \] Now the equation is: \[ -12 + 2x = 6 - 3x \] Next, let's move all \(x\) terms to one side and constant terms to the other side. We'll add \(3x\) and \(12\) to both sides: \[ 2x + 3x = 6 + 12 \] \[ 5x = 18 \] Now, divide by \(5\): \[ x = \frac{18}{5} \] Thus, the solution for \(x\) is \(\frac{18}{5}\).
