Solve the Inequality for t 12t-2<-5t+36

$12 t - 2 < - 5 t + 36$

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

Add $5 t$ to both sides of the inequality.

$12 t - 2 + 5 t < 36$

Add $12 t$ and $5 t$ .

$17 t - 2 < 36$

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

Add $2$ to both sides of the inequality.

$17 t < 36 + 2$

Add $36$ and $2$ .

$17 t < 38$

Divide each term in $17 t < 38$ by $17$ and simplify.

Divide each term in $17 t < 38$ by $17$ .

$\frac{17 t}{17} < \frac{38}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 t}{17} < \frac{38}{17}$

Divide $t$ by $1$ .

$t < \frac{38}{17}$

The result can be shown in multiple forms.

Inequality Form:

$t < \frac{38}{17}$

Interval Notation:

$(- \infty, \frac{38}{17})$