Questions: (x-2)/15-2/5=(-2x+3)/3

(x-2)/15-2/5=(-2x+3)/3
Transcript text: $\frac{x-2}{15}-\frac{2}{5}=\frac{-2 x+3}{3}$
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Solution

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Solution Steps

To solve the equation \(\frac{x-2}{15}-\frac{2}{5}=\frac{-2 x+3}{3}\), we need to find the value of \(x\). The approach involves:

  1. Finding a common denominator for the fractions.
  2. Simplifying the equation by eliminating the fractions.
  3. Solving the resulting linear equation for \(x\).
Step 1: Set Up the Equation

We start with the given equation: \[ \frac{x-2}{15} - \frac{2}{5} = \frac{-2x+3}{3} \]

Step 2: Find a Common Denominator

To eliminate the fractions, we find a common denominator. The least common multiple of 15, 5, and 3 is 15. We rewrite each term with a denominator of 15: \[ \frac{x-2}{15} - \frac{6}{15} = \frac{-10x + 15}{15} \]

Step 3: Combine the Fractions

Combine the fractions on the left-hand side: \[ \frac{x-2-6}{15} = \frac{-10x + 15}{15} \] Simplify the numerator: \[ \frac{x-8}{15} = \frac{-10x + 15}{15} \]

Step 4: Eliminate the Denominator

Since the denominators are the same, we can equate the numerators: \[ x - 8 = -10x + 15 \]

Step 5: Solve for \(x\)

Rearrange the equation to isolate \(x\): \[ x + 10x = 15 + 8 \] \[ 11x = 23 \] \[ x = \frac{23}{11} \approx 2.0909 \]

Final Answer

\[ \boxed{x \approx 2.0909} \]

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