Solve 8(t+2)+3>2(t+4)+6

$$8 ( t + 2 ) + 3 > 2 ( t + 4 ) + 6$$

Solve for t

$$t>-\frac{5}{6}$$

Solution Steps

Use the distributive property to multiply 8 by t+2.

$$8t+16+3>2\left(t+4\right)+6$$

Add 16 and 3 to get 19.

$$8t+19>2\left(t+4\right)+6$$

Use the distributive property to multiply 2 by t+4.

$$8t+19>2t+8+6$$

Add 8 and 6 to get 14.

$$8t+19>2t+14$$

Subtract 2t from both sides.

$$8t+19-2t>14$$

Combine 8t and -2t to get 6t.

$$6t+19>14$$

Subtract 19 from both sides.

$$6t>14-19$$

Subtract 19 from 14 to get -5.

$$6t>-5$$

Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.

$$t>-\frac{5}{6}$$