Solve x+4(x-2(x+7))=5(1+2(x-1))

$$x+4(x-2(x+7))=5(1+2(x-1))$$

Solve for x

$$x = -\frac{51}{13} = -3\frac{12}{13} \approx -3.923076923$$

Steps for Solving Linear Equation

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

$$x+4\left(x-2x-14\right)=5\left(1+2\left(x-1\right)\right)$$

Combine x and -2x to get -x.

$$x+4\left(-x-14\right)=5\left(1+2\left(x-1\right)\right)$$

Use the distributive property to multiply 4 by -x-14.

$$x-4x-56=5\left(1+2\left(x-1\right)\right)$$

Combine x and -4x to get -3x.

$$-3x-56=5\left(1+2\left(x-1\right)\right)$$

Use the distributive property to multiply 2 by x-1.

$$-3x-56=5\left(1+2x-2\right)$$

Subtract 2 from 1 to get -1.

$$-3x-56=5\left(-1+2x\right)$$

Use the distributive property to multiply 5 by -1+2x.

$$-3x-56=-5+10x$$

Subtract 10x from both sides.

$$-3x-56-10x=-5$$

Combine -3x and -10x to get -13x.

$$-13x-56=-5$$

Add 56 to both sides.

$$-13x=-5+56$$

Add -5 and 56 to get 51.

$$-13x=51$$

Divide both sides by -13.

$$x=\frac{51}{-13}$$

Fraction \frac{51}{-13} can be rewritten as -\frac{51}{13} by extracting the negative sign.

$$x=-\frac{51}{13}$$