Solve 5-3(2x-7)=4(x-2)-(7-x)

$$5 - 3 ( 2 x - 7 ) = 4 ( x - 2 ) - ( 7 - x )$$

Solve for x

$$x = \frac{41}{11} = 3\frac{8}{11} \approx 3.727272727$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by 2x-7.

$$5-6x+21=4\left(x-2\right)-\left(7-x\right)$$

Add 5 and 21 to get 26.

$$26-6x=4\left(x-2\right)-\left(7-x\right)$$

Use the distributive property to multiply 4 by x-2.

$$26-6x=4x-8-\left(7-x\right)$$

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

$$26-6x=4x-8-7-\left(-x\right)$$

The opposite of -x is x.

$$26-6x=4x-8-7+x$$

Subtract 7 from -8 to get -15.

$$26-6x=4x-15+x$$

Combine 4x and x to get 5x.

$$26-6x=5x-15$$

Subtract 5x from both sides.

$$26-6x-5x=-15$$

Combine -6x and -5x to get -11x.

$$26-11x=-15$$

Subtract 26 from both sides.

$$-11x=-15-26$$

Subtract 26 from -15 to get -41.

$$-11x=-41$$

Divide both sides by -11.

$$x=\frac{-41}{-11}$$

Fraction \frac{-41}{-11} can be simplified to \frac{41}{11} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{41}{11}$$