Solve 5x-7/4-9x-4/5=2-3x+11

$$\frac { 5 x - 7 } { 4 } - 9 \frac { x - 4 } { 5 } = 2 - 3 x + 11$$

Solve for x

$$x = \frac{151}{49} = 3\frac{4}{49} \approx 3.081632653$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,5.

$$5\left(5x-7\right)-36\left(x-4\right)=40-60x+220$$

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

$$25x-35-36\left(x-4\right)=40-60x+220$$

Use the distributive property to multiply -36 by x-4.

$$25x-35-36x+144=40-60x+220$$

Combine 25x and -36x to get -11x.

$$-11x-35+144=40-60x+220$$

Add -35 and 144 to get 109.

$$-11x+109=40-60x+220$$

Add 40 and 220 to get 260.

$$-11x+109=260-60x$$

Add 60x to both sides.

$$-11x+109+60x=260$$

Combine -11x and 60x to get 49x.

$$49x+109=260$$

Subtract 109 from both sides.

$$49x=260-109$$

Subtract 109 from 260 to get 151.

$$49x=151$$

Divide both sides by 49.

$$x=\frac{151}{49}$$