Solve 74-29t-(50-43s-30t+42r)=(7t-43r+44s+24)

$$74 - 29 t - ( 50 - 43 s - 30 t + 42 r ) = ( 7 t - 43 r + 44 s + 24 )$$

Solve for r

$$r=s+6t$$

Solution Steps

To find the opposite of 50-43s-30t+42r, find the opposite of each term.

$$74-29t-50+43s+30t-42r=7t-43r+44s+24$$

Subtract 50 from 74 to get 24.

$$24-29t+43s+30t-42r=7t-43r+44s+24$$

Combine -29t and 30t to get t.

$$24+t+43s-42r=7t-43r+44s+24$$

Add 43r to both sides.

$$24+t+43s-42r+43r=7t+44s+24$$

Combine -42r and 43r to get r.

$$24+t+43s+r=7t+44s+24$$

Subtract 24 from both sides.

$$t+43s+r=7t+44s+24-24$$

Subtract 24 from 24 to get 0.

$$t+43s+r=7t+44s$$

Subtract t from both sides.

$$43s+r=7t+44s-t$$

Combine 7t and -t to get 6t.

$$43s+r=6t+44s$$

Subtract 43s from both sides.

$$r=6t+44s-43s$$

Combine 44s and -43s to get s.

$$r=6t+s$$

Solve for s

$$s=r-6t$$

Steps for Solving Linear Equation

To find the opposite of 50-43s-30t+42r, find the opposite of each term.

$$74-29t-50+43s+30t-42r=7t-43r+44s+24$$

Subtract 50 from 74 to get 24.

$$24-29t+43s+30t-42r=7t-43r+44s+24$$

Combine -29t and 30t to get t.

$$24+t+43s-42r=7t-43r+44s+24$$

Subtract 44s from both sides.

$$24+t+43s-42r-44s=7t-43r+24$$

Combine 43s and -44s to get -s.

$$24+t-s-42r=7t-43r+24$$

Subtract 24 from both sides.

$$t-s-42r=7t-43r+24-24$$

Subtract 24 from 24 to get 0.

$$t-s-42r=7t-43r$$

Subtract t from both sides.

$$-s-42r=7t-43r-t$$

Combine 7t and -t to get 6t.

$$-s-42r=6t-43r$$

Add 42r to both sides.

$$-s=6t-43r+42r$$

Combine -43r and 42r to get -r.

$$-s=6t-r$$

Divide both sides by -1.

$$\frac{-s}{-1}=\frac{6t-r}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$s=\frac{6t-r}{-1}$$

Divide 6t-r by -1.

$$s=r-6t$$