Find the value of x that satisfies the equation (4x + 7)/2 - (3x - 5)/3 = 5.

Find the value of $x$ that satisfies the equation $\frac{4 x + 7}{2} - \frac{3 x - 5}{3} = 5$ .

hard MCQ 3 marks Class 8 · Mathematics · Linear Equations in One Variable

Answer

-1/6

The correct answer is -1/6 — Divide by $6$ : $x = - \frac{1}{6}$ .

Find common denominator $6$ and rewrite: $\frac{3 ( 4 x + 7 )}{6} - \frac{2 ( 3 x - 5 )}{6} = 5$ .
Simplify numerators: $\frac{12 x + 21}{6} - \frac{6 x - 10}{6} = 5$ .
Combine over common denominator: $\frac{( 12 x + 21 ) - ( 6 x - 10 )}{6} = 5$ .
Simplify numerator: $\frac{6 x + 31}{6} = 5$ .
Multiply both sides by $6$ : $6 x + 31 = 30$ .
Subtract $31$ : $6 x = - 1$ .
Divide by $6$ : $x = - \frac{1}{6}$ .

Common mistake: Incorrect sign when combining fractions

Concept tested: Solving fractional linear equations with subtraction