Solve 7x+11/2-13x-5/3=5-7x-3/4

$$\frac { 7 x + 11 } { 2 } - \frac { 13 x - 5 } { 3 } = 5 - \frac { 7 x - 3 } { 4 }$$

Solve for x

$$x = -\frac{17}{11} = -1\frac{6}{11} \approx -1.545454545$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 12, the least common multiple of 2,3,4.

$$6\left(7x+11\right)-4\left(13x-5\right)=60-3\left(7x-3\right)$$

Use the distributive property to multiply 6 by 7x+11.

$$42x+66-4\left(13x-5\right)=60-3\left(7x-3\right)$$

Use the distributive property to multiply -4 by 13x-5.

$$42x+66-52x+20=60-3\left(7x-3\right)$$

Combine 42x and -52x to get -10x.

$$-10x+66+20=60-3\left(7x-3\right)$$

Add 66 and 20 to get 86.

$$-10x+86=60-3\left(7x-3\right)$$

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

$$-10x+86=60-21x+9$$

Add 60 and 9 to get 69.

$$-10x+86=69-21x$$

Add 21x to both sides.

$$-10x+86+21x=69$$

Combine -10x and 21x to get 11x.

$$11x+86=69$$

Subtract 86 from both sides.

$$11x=69-86$$

Subtract 86 from 69 to get -17.

$$11x=-17$$

Divide both sides by 11.

$$x=\frac{-17}{11}$$

Fraction \frac{-17}{11} can be rewritten as -\frac{17}{11} by extracting the negative sign.

$$x=-\frac{17}{11}$$