Solve 5(2x+3)-(x-2)=2(x-2)-(2x-2)-(2x-3)

$$5(2x+3)-(x-2)=2(x-2)-(2x-2)-(2x-3)$$

Solve for x

$$x = -\frac{16}{11} = -1\frac{5}{11} \approx -1.454545455$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2x+3.

$$10x+15-\left(x-2\right)=2\left(x-2\right)-\left(2x-2\right)-\left(2x-3\right)$$

To find the opposite of x-2, find the opposite of each term.

$$10x+15-x-\left(-2\right)=2\left(x-2\right)-\left(2x-2\right)-\left(2x-3\right)$$

The opposite of -2 is 2.

$$10x+15-x+2=2\left(x-2\right)-\left(2x-2\right)-\left(2x-3\right)$$

Combine 10x and -x to get 9x.

$$9x+15+2=2\left(x-2\right)-\left(2x-2\right)-\left(2x-3\right)$$

Add 15 and 2 to get 17.

$$9x+17=2\left(x-2\right)-\left(2x-2\right)-\left(2x-3\right)$$

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

$$9x+17=2x-4-\left(2x-2\right)-\left(2x-3\right)$$

To find the opposite of 2x-2, find the opposite of each term.

$$9x+17=2x-4-2x-\left(-2\right)-\left(2x-3\right)$$

The opposite of -2 is 2.

$$9x+17=2x-4-2x+2-\left(2x-3\right)$$

Combine 2x and -2x to get 0.

$$9x+17=-4+2-\left(2x-3\right)$$

Add -4 and 2 to get -2.

$$9x+17=-2-\left(2x-3\right)$$

To find the opposite of 2x-3, find the opposite of each term.

$$9x+17=-2-2x-\left(-3\right)$$

The opposite of -3 is 3.

$$9x+17=-2-2x+3$$

Add -2 and 3 to get 1.

$$9x+17=1-2x$$

Add 2x to both sides.

$$9x+17+2x=1$$

Combine 9x and 2x to get 11x.

$$11x+17=1$$

Subtract 17 from both sides.

$$11x=1-17$$

Subtract 17 from 1 to get -16.

$$11x=-16$$

Divide both sides by 11.

$$x=\frac{-16}{11}$$

Fraction \frac{-16}{11} can be rewritten as -\frac{16}{11} by extracting the negative sign.

$$x=-\frac{16}{11}$$