Solve {x-2.5(7-4x)=x-7(4+x)

$$\{ x - 2.5 ( 7 - 4 x ) = x - 7 ( 4 + x )$$

Solve for x

$$x=-\frac{21}{34}\approx -0.617647059$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2.5 by 7-4x.

$$x-17.5+10x=x-7\left(4+x\right)$$

Combine x and 10x to get 11x.

$$11x-17.5=x-7\left(4+x\right)$$

Use the distributive property to multiply -7 by 4+x.

$$11x-17.5=x-28-7x$$

Combine x and -7x to get -6x.

$$11x-17.5=-6x-28$$

Add 6x to both sides.

$$11x-17.5+6x=-28$$

Combine 11x and 6x to get 17x.

$$17x-17.5=-28$$

Add 17.5 to both sides.

$$17x=-28+17.5$$

Add -28 and 17.5 to get -10.5.

$$17x=-10.5$$

Divide both sides by 17.

$$x=\frac{-10.5}{17}$$

Expand \frac{-10.5}{17} by multiplying both numerator and the denominator by 10.

$$x=\frac{-105}{170}$$

Reduce the fraction \frac{-105}{170} to lowest terms by extracting and canceling out 5.

$$x=-\frac{21}{34}$$