Solve 3(x-2)=4(-x+3)

$$3(x-2)=4(-x+3)$$

Solve for x

$$x = \frac{18}{7} = 2\frac{4}{7} \approx 2.571428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x-2.

$$3x-6=4\left(-x+3\right)$$

Use the distributive property to multiply 4 by -x+3.

$$3x-6=4\left(-x\right)+12$$

Subtract 4\left(-x\right) from both sides.

$$3x-6-4\left(-x\right)=12$$

Multiply -1 and 4 to get -4.

$$3x-6-4\left(-1\right)x=12$$

Multiply -4 and -1 to get 4.

$$3x-6+4x=12$$

Combine 3x and 4x to get 7x.

$$7x-6=12$$

Add 6 to both sides.

$$7x=12+6$$

Add 12 and 6 to get 18.

$$7x=18$$

Divide both sides by 7.

$$x=\frac{18}{7}$$