Solve {l}{2x+4(3-2x)=3(2x+2)/6+4}{4z+5=-3z-8}{1/2-1/8q=q-1/4}

$$\left. \begin{array} { l } { 2 x + 4 ( 3 - 2 x ) = \frac { 3 ( 2 x + 2 ) } { 6 } + 4 } \\ { 4 z + 5 = - 3 z - 8 } \\ { \frac { 1 } { 2 } - \frac { 1 } { 8 } q = \frac { q - 1 } { 4 } } \end{array} \right.$$

Solve for x, z, q

$$x=1$$

$$z = -\frac{13}{7} = -1\frac{6}{7} \approx -1.857142857$$

$$q=2$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 6.

$$12x+24\left(3-2x\right)=3\left(2x+2\right)+24$$

Use the distributive property to multiply 24 by 3-2x.

$$12x+72-48x=3\left(2x+2\right)+24$$

Combine 12x and -48x to get -36x.

$$-36x+72=3\left(2x+2\right)+24$$

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

$$-36x+72=6x+6+24$$

Add 6 and 24 to get 30.

$$-36x+72=6x+30$$

Subtract 6x from both sides.

$$-36x+72-6x=30$$

Combine -36x and -6x to get -42x.

$$-42x+72=30$$

Subtract 72 from both sides.

$$-42x=30-72$$

Subtract 72 from 30 to get -42.

$$-42x=-42$$

Divide both sides by -42.

$$x=\frac{-42}{-42}$$

Divide -42 by -42 to get 1.

$$x=1$$

Consider the second equation. Add 3z to both sides.

$$4z+5+3z=-8$$

Combine 4z and 3z to get 7z.

$$7z+5=-8$$

Subtract 5 from both sides.

$$7z=-8-5$$

Subtract 5 from -8 to get -13.

$$7z=-13$$

Divide both sides by 7.

$$z=-\frac{13}{7}$$

Consider the third equation. Multiply both sides of the equation by 8, the least common multiple of 2,8,4.

$$4-q=2\left(q-1\right)$$

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

$$4-q=2q-2$$

Subtract 2q from both sides.

$$4-q-2q=-2$$

Combine -q and -2q to get -3q.

$$4-3q=-2$$

Subtract 4 from both sides.

$$-3q=-2-4$$

Subtract 4 from -2 to get -6.

$$-3q=-6$$

Divide both sides by -3.

$$q=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$q=2$$

The system is now solved.

$$x=1 z=-\frac{13}{7} q=2$$