Question

$\frac{x + 3}{2} + \frac{x - 2}{3} = 5$
​

Answer 1

Answer:

$\frac{x + 3}{2} + \frac{x - 2}{3} = 5 \\ \\ \frac{3x + 9 + 2x - 4}{6} = 5 \\ \frac{5x + 5}{6} = 5 \\ 5x + 5 = 5 \times 6 \\ 5x + 5 = 30 \\ 5 x = 30 - 5 \\ 5x = 25 \\ x = \frac{25}{5} \\ x = 5$

Answer 2

Find common denominator

$\frac{x + 3}{2} + \frac{x - 2}{3} = 5$

$\frac{(x + 3)}{6} + \frac{2(x - 2)}{6} = 5$

Combine fractions with common denominator

$\frac{3(x + 3) + 2(x - 6)} {6} = 5$

Distribute

$\frac{3x + 9 + 2(x - 6)} {6} = 5$

$\frac{3x + 9 + 2x - 4} {6} = 5$

Subtract the numbers

$\frac{3+5 + 2x}{6} =5$

Combine like terms

$\frac{5x + 5}{6} = 5$

Multiply all terms by the same value to eliminate fraction denominators

$6( \frac{5x + 5}{6} ) = 6 \times 5$

Cancel multiplied terms that are in the denominator

$5x + 5 = 6 \times 5$

Multiply the numbers

$5x + 5 = 30$

Subtract 5 from both sides of the equation

$5x + 5 - 5 = 30 - 5$

Simplify

Subtract the numbers

$5x = 30 - 5$

$5x = 25$

Divide both sides of the equation by the same term

$\frac{5x}{5} = \frac{25}{5}$

Simplify

Cancel terms that are in both the numerator and denominator

$x = \frac{25}{5}$

Divide the numbers

$x = 5$

Answer is X= 5