Solve 2x+5/7=4x-7/5

$$\frac { 2 x + 5 } { 7 } = \frac { 4 x - 7 } { 5 }$$

Solve for x

$$x = \frac{37}{9} = 4\frac{1}{9} \approx 4.111111111$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 35, the least common multiple of 7,5.

$$5\left(2x+5\right)=7\left(4x-7\right)$$

Use the distributive property to multiply 5 by 2x+5.

$$10x+25=7\left(4x-7\right)$$

Use the distributive property to multiply 7 by 4x-7.

$$10x+25=28x-49$$

Subtract 28x from both sides.

$$10x+25-28x=-49$$

Combine 10x and -28x to get -18x.

$$-18x+25=-49$$

Subtract 25 from both sides.

$$-18x=-49-25$$

Subtract 25 from -49 to get -74.

$$-18x=-74$$

Divide both sides by -18.

$$x=\frac{-74}{-18}$$

Reduce the fraction \frac{-74}{-18} to lowest terms by extracting and canceling out -2.

$$x=\frac{37}{9}$$