Solve the Inequality for t 7t+15<3t-8

$7 t + 15 < 3 t - 8$

Move all terms containing $t$ to the left side of the inequality.

Subtract $3 t$ from both sides of the inequality.

$7 t + 15 - 3 t < - 8$

Subtract $3 t$ from $7 t$ .

$4 t + 15 < - 8$

Move all terms not containing $t$ to the right side of the inequality.

Subtract $15$ from both sides of the inequality.

$4 t < - 8 - 15$

Subtract $15$ from $- 8$ .

$4 t < - 23$

Divide each term in $4 t < - 23$ by $4$ and simplify.

Divide each term in $4 t < - 23$ by $4$ .

$\frac{4 t}{4} < \frac{- 23}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 t}{4} < \frac{- 23}{4}$

Divide $t$ by $1$ .

$t < \frac{- 23}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$t < - \frac{23}{4}$

The result can be shown in multiple forms.

Inequality Form:

$t < - \frac{23}{4}$

Interval Notation:

$(- \infty, - \frac{23}{4})$