Question
Solve. \[ 6.5 x-4.32=5.2-5.4 x \] The solution is \( x=\square \). (Type an integer or a decimal.)
Ask by Kelly Little. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 0.8 \)
Solution
To solve the equation 6.5x - 4.32 = 5.2 - 5.4x, follow these steps:
1. Begin with the original equation:
6.5x - 4.32 = 5.2 - 5.4x
2. Add 5.4x to both sides to bring the x-terms together:
6.5x + 5.4x - 4.32 = 5.2
3. Combine like terms:
11.9x - 4.32 = 5.2
4. Add 4.32 to both sides to isolate the x-term:
11.9x = 5.2 + 4.32
11.9x = 9.52
5. Divide both sides by 11.9 to solve for x:
x = 9.52 / 11.9
x = 0.8
Thus, the solution is x = 0.8.
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Simplify this solution Bonus Knowledge
To solve for \( x \): First, let's move all terms involving \( x \) to one side and constant terms to the other side. \[ 6.5x + 5.4x = 5.2 + 4.32 \] Combine like terms: \[ 11.9x = 9.52 \] Now, divide both sides by \( 11.9 \): \[ x = \frac{9.52}{11.9} \approx 0.801679 \] Thus, the solution is \( x \approx 0.80 \) (rounded to two decimal places).
