Solve (2x+3)-(5x-7)/6x+11=-8/3

$$\frac { ( 2 x + 3 ) - ( 5 x - 7 ) } { 6 x + 11 } = \frac { - 8 } { 3 }$$

Solve for x

$$x = -\frac{118}{39} = -3\frac{1}{39} \approx -3.025641026$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{11}{6} since division by zero is not defined. Multiply both sides of the equation by 3\left(6x+11\right), the least common multiple of 6x+11,3.

$$3\left(2x+3-\left(5x-7\right)\right)=\left(6x+11\right)\left(-8\right)$$

To find the opposite of 5x-7, find the opposite of each term.

$$3\left(2x+3-5x+7\right)=\left(6x+11\right)\left(-8\right)$$

Combine 2x and -5x to get -3x.

$$3\left(-3x+3+7\right)=\left(6x+11\right)\left(-8\right)$$

Add 3 and 7 to get 10.

$$3\left(-3x+10\right)=\left(6x+11\right)\left(-8\right)$$

Use the distributive property to multiply 3 by -3x+10.

$$-9x+30=\left(6x+11\right)\left(-8\right)$$

Use the distributive property to multiply 6x+11 by -8.

$$-9x+30=-48x-88$$

Add 48x to both sides.

$$-9x+30+48x=-88$$

Combine -9x and 48x to get 39x.

$$39x+30=-88$$

Subtract 30 from both sides.

$$39x=-88-30$$

Subtract 30 from -88 to get -118.

$$39x=-118$$

Divide both sides by 39.

$$x=\frac{-118}{39}$$

Fraction \frac{-118}{39} can be rewritten as -\frac{118}{39} by extracting the negative sign.

$$x=-\frac{118}{39}$$