Solve 21-[5x-(3x-1)]=5x-12

$$21 - [ 5 x - ( 3 x - 1 ) ] = 5 x - 12$$

Solve for x

$$x = \frac{32}{7} = 4\frac{4}{7} \approx 4.571428571$$

Steps for Solving Linear Equation

To find the opposite of 3x-1, find the opposite of each term.

$$21-\left(5x-3x-\left(-1\right)\right)=5x-12$$

The opposite of -1 is 1.

$$21-\left(5x-3x+1\right)=5x-12$$

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

$$21-\left(2x+1\right)=5x-12$$

To find the opposite of 2x+1, find the opposite of each term.

$$21-2x-1=5x-12$$

Subtract 1 from 21 to get 20.

$$20-2x=5x-12$$

Subtract 5x from both sides.

$$20-2x-5x=-12$$

Combine -2x and -5x to get -7x.

$$20-7x=-12$$

Subtract 20 from both sides.

$$-7x=-12-20$$

Subtract 20 from -12 to get -32.

$$-7x=-32$$

Divide both sides by -7.

$$x=\frac{-32}{-7}$$

Fraction \frac{-32}{-7} can be simplified to \frac{32}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{32}{7}$$