Solve for t 7t+1<=t+4

$7 t + 1 \leq t + 4$

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

Subtract $t$ from both sides of the inequality.

$7 t + 1 - t \leq 4$

Subtract $t$ from $7 t$ .

$6 t + 1 \leq 4$

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

Subtract $1$ from both sides of the inequality.

$6 t \leq 4 - 1$

Subtract $1$ from $4$ .

$6 t \leq 3$

Divide each term in $6 t \leq 3$ by $6$ and simplify.

Divide each term in $6 t \leq 3$ by $6$ .

$\frac{6 t}{6} \leq \frac{3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 t}{6} \leq \frac{3}{6}$

Divide $t$ by $1$ .

$t \leq \frac{3}{6}$

Simplify the right side.

Cancel the common factor of $3$ and $6$ .

Factor $3$ out of $3$ .

$t \leq \frac{3 (1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

$t \leq \frac{3 \cdot 1}{3 \cdot 2}$

Cancel the common factor.

$t \leq \frac{3 \cdot 1}{3 \cdot 2}$

Rewrite the expression.

$t \leq \frac{1}{2}$

The result can be shown in multiple forms.

Inequality Form:

$t \leq \frac{1}{2}$

Interval Notation:

$(- \infty, \frac{1}{2}]$