Solve 6x+4/5 + 4x−1/3 + 3x+2/5

Question

ScanSolve AI Tutor · Accepted Answer

Okay, Nisa, let's solve question 2.1.

The equation is:

\frac{x+2}{6} + \frac{4x-1}{3} = \frac{3x+2}{5}

Find a common denominator for the fractions on the left side.
The LCM of 6 and 3 is 6.
$\frac{x+2}{6} + \frac{2(4x-1)}{2 \cdot 3} = \frac{3x+2}{5}$ $\frac{x+2}{6} + \frac{8x-2}{6} = \frac{3x+2}{5}$
Combine the fractions on the left side.
$\frac{(x+2) + (8x-2)}{6} = \frac{3x+2}{5}$ $\frac{x+8x+2-2}{6} = \frac{3x+2}{5}$ $\frac{9x}{6} = \frac{3x+2}{5}$
Simplify the fraction on the left side and cross-multiply.
$\frac{3x}{2} = \frac{3x+2}{5}$ $5(3x) = 2(3x+2)$
Expand and solve for $x$ .
$15x = 6x + 4$ $15x - 6x = 4$ $9x = 4$ $x = \frac{4}{9}$

Solve 6x+4/5 + 4x-1/3 + 3x+2/5