$$\frac { 2 x + 5 x + 2 } { 3 x - 1 x - 3 } = \frac { 3 } { 2 }$$
Solve for x
$x = -\frac{13}{8} = -1\frac{5}{8} = -1.625$
Steps for Solving Linear Equation
Variable $x$ cannot be equal to $\frac{3}{2}$ since division by zero is not defined. Multiply both sides of the equation by $2\left(2x-3\right)$, the least common multiple of $3x-x-3,2$.
$$2\left(2x+5x+2\right)=3\left(2x-3\right)$$
Combine $2x$ and $5x$ to get $7x$.
$$2\left(7x+2\right)=3\left(2x-3\right)$$
Use the distributive property to multiply $2$ by $7x+2$.
$$14x+4=3\left(2x-3\right)$$
Use the distributive property to multiply $3$ by $2x-3$.
$$14x+4=6x-9$$
Subtract $6x$ from both sides.
$$14x+4-6x=-9$$
Combine $14x$ and $-6x$ to get $8x$.
$$8x+4=-9$$
Subtract $4$ from both sides.
$$8x=-9-4$$
Subtract $4$ from $-9$ to get $-13$.
$$8x=-13$$
Divide both sides by $8$.
$$x=\frac{-13}{8}$$
Fraction $\frac{-13}{8}$ can be rewritten as $-\frac{13}{8}$ by extracting the negative sign.
