Solve s-4/2+s-3/2=2s-5/3-3s-22/5

$$\frac { s - 4 } { 2 } + \frac { s - 3 } { 2 } = \frac { 2 s - 5 } { 3 } - \frac { 3 s - 22 } { 5 }$$

Solve for s

$$s = \frac{187}{28} = 6\frac{19}{28} \approx 6.678571429$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 2,3,5.

$$15\left(s-4\right)+15\left(s-3\right)=10\left(2s-5\right)-6\left(3s-22\right)$$

Use the distributive property to multiply 15 by s-4.

$$15s-60+15\left(s-3\right)=10\left(2s-5\right)-6\left(3s-22\right)$$

Use the distributive property to multiply 15 by s-3.

$$15s-60+15s-45=10\left(2s-5\right)-6\left(3s-22\right)$$

Combine 15s and 15s to get 30s.

$$30s-60-45=10\left(2s-5\right)-6\left(3s-22\right)$$

Subtract 45 from -60 to get -105.

$$30s-105=10\left(2s-5\right)-6\left(3s-22\right)$$

Use the distributive property to multiply 10 by 2s-5.

$$30s-105=20s-50-6\left(3s-22\right)$$

Use the distributive property to multiply -6 by 3s-22.

$$30s-105=20s-50-18s+132$$

Combine 20s and -18s to get 2s.

$$30s-105=2s-50+132$$

Add -50 and 132 to get 82.

$$30s-105=2s+82$$

Subtract 2s from both sides.

$$30s-105-2s=82$$

Combine 30s and -2s to get 28s.

$$28s-105=82$$

Add 105 to both sides.

$$28s=82+105$$

Add 82 and 105 to get 187.

$$28s=187$$

Divide both sides by 28.

$$s=\frac{187}{28}$$