$$\left. \begin{array} { l } { \frac { 2 x - 5 } { 7 x - 3 } = \frac { 5 } { 4 } } \end{array} \right.$$
Solve for x
$x=-\frac{5}{27}\approx -0.185185185$
Steps for Solving Linear Equation
Variable $x$ cannot be equal to $\frac{3}{7}$ since division by zero is not defined. Multiply both sides of the equation by $4\left(7x-3\right)$, the least common multiple of $7x-3,4$.
$$4\left(2x-5\right)=5\left(7x-3\right)$$
Use the distributive property to multiply $4$ by $2x-5$.
$$8x-20=5\left(7x-3\right)$$
Use the distributive property to multiply $5$ by $7x-3$.
$$8x-20=35x-15$$
Subtract $35x$ from both sides.
$$8x-20-35x=-15$$
Combine $8x$ and $-35x$ to get $-27x$.
$$-27x-20=-15$$
Add $20$ to both sides.
$$-27x=-15+20$$
Add $-15$ and $20$ to get $5$.
$$-27x=5$$
Divide both sides by $-27$.
$$x=\frac{5}{-27}$$
Fraction $\frac{5}{-27}$ can be rewritten as $-\frac{5}{27}$ by extracting the negative sign.
