Solve for x 1/2x-3/7=1-x/3

Problem

1/2*x−3/7=1−x/3

Solution

1. Identify the least common multiple (LCM) of the denominators 2 7 and 3 to clear the fractions.

2. Calculate the LCM, which is 42

3. Multiply every term in the equation by 42 to eliminate the denominators.

42⋅1/2*x−42⋅3/7=42⋅1−42⋅x/3

4. Simplify each term after multiplication.

21*x−18=42−14*x

5. Add 14*x to both sides to group the variable terms.

35*x−18=42

6. Add 18 to both sides to isolate the term with the variable.

35*x=60

7. Divide both sides by 35 to solve for x

x=60/35

8. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 5

x=12/7

Final Answer

1/2*x−3/7=1−x/3⇒x=12/7

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