Solve for x (x+1)/3+(x+2)/7=5

Problem

(x+1)/3+(x+2)/7=5

Solution

1. Find the least common denominator of the fractions on the left side, which is 3×7=21

2. Multiply every term in the equation by 21 to eliminate the denominators.

21*((x+1)/3)+21*((x+2)/7)=21*(5)

3. Simplify the terms by dividing the common factors.

7*(x+1)+3*(x+2)=105

4. Distribute the constants into the parentheses.

7*x+7+3*x+6=105

5. Combine like terms on the left side of the equation.

10*x+13=105

6. Isolate the variable term by subtracting 13 from both sides.

10*x=92

7. Solve for x by dividing both sides by 10

x=92/10

8. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, 2

x=46/5

Final Answer

(x+1)/3+(x+2)/7=5⇒x=46/5

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