Solve {l}{4{(3m+2)}-5{(6m-1)}=9{(m-8)}-6{(7m-4)}}{n=4m}{o=n}{p=o}{q=p}{text{Solvefor}rtext{where}}{r=q}

$$\left. \begin{array} { l } { 4 {(3 m + 2)} - 5 {(6 m - 1)} = 9 {(m - 8)} - 6 {(7 m - 4)} }\\ { n = 4 m }\\ { o = n }\\ { p = o }\\ { q = p }\\ { \text{Solve for } r \text{ where} } \\ { r = q } \end{array} \right.$$

Solve for m, n, o, p, q, r

$$r = -\frac{244}{15} = -16\frac{4}{15} \approx -16.266666667$$

Solution Steps

Consider the first equation. Use the distributive property to multiply 4 by 3m+2.

$$12m+8-5\left(6m-1\right)=9\left(m-8\right)-6\left(7m-4\right)$$

Use the distributive property to multiply -5 by 6m-1.

$$12m+8-30m+5=9\left(m-8\right)-6\left(7m-4\right)$$

Combine 12m and -30m to get -18m.

$$-18m+8+5=9\left(m-8\right)-6\left(7m-4\right)$$

Add 8 and 5 to get 13.

$$-18m+13=9\left(m-8\right)-6\left(7m-4\right)$$

Use the distributive property to multiply 9 by m-8.

$$-18m+13=9m-72-6\left(7m-4\right)$$

Use the distributive property to multiply -6 by 7m-4.

$$-18m+13=9m-72-42m+24$$

Combine 9m and -42m to get -33m.

$$-18m+13=-33m-72+24$$

Add -72 and 24 to get -48.

$$-18m+13=-33m-48$$

Add 33m to both sides.

$$-18m+13+33m=-48$$

Combine -18m and 33m to get 15m.

$$15m+13=-48$$

Subtract 13 from both sides.

$$15m=-48-13$$

Subtract 13 from -48 to get -61.

$$15m=-61$$

Divide both sides by 15.

$$m=-\frac{61}{15}$$

Consider the second equation. Insert the known values of variables into the equation.

$$n=4\left(-\frac{61}{15}\right)$$

Multiply 4 and -\frac{61}{15} to get -\frac{244}{15}.

$$n=-\frac{244}{15}$$

Consider the third equation. Insert the known values of variables into the equation.

$$o=-\frac{244}{15}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$p=-\frac{244}{15}$$

Consider the fifth equation. Insert the known values of variables into the equation.

$$q=-\frac{244}{15}$$

Consider the equation (6). Insert the known values of variables into the equation.

$$r=-\frac{244}{15}$$

The system is now solved.

$$m=-\frac{61}{15} n=-\frac{244}{15} o=-\frac{244}{15} p=-\frac{244}{15} q=-\frac{244}{15} r=-\frac{244}{15}$$