Solve 2x-5/9=3x-7/7

$$\frac { 2 x - 5 } { 9 } = \frac { 3 x - 7 } { 7 }$$

Solve for x

$$x = \frac{28}{13} = 2\frac{2}{13} \approx 2.153846154$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 63, the least common multiple of 9,7.

$$7\left(2x-5\right)=9\left(3x-7\right)$$

Use the distributive property to multiply 7 by 2x-5.

$$14x-35=9\left(3x-7\right)$$

Use the distributive property to multiply 9 by 3x-7.

$$14x-35=27x-63$$

Subtract 27x from both sides.

$$14x-35-27x=-63$$

Combine 14x and -27x to get -13x.

$$-13x-35=-63$$

Add 35 to both sides.

$$-13x=-63+35$$

Add -63 and 35 to get -28.

$$-13x=-28$$

Divide both sides by -13.

$$x=\frac{-28}{-13}$$

Fraction \frac{-28}{-13} can be simplified to \frac{28}{13} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{28}{13}$$