Solve the Inequality for t 6t+3<7t+10

$6 t + 3 < 7 t + 10$

Step 1

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

Subtract $7 t$ from both sides of the inequality.

$6 t + 3 - 7 t < 10$

Subtract $7 t$ from $6 t$ .

$- t + 3 < 10$

Step 2

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

Subtract $3$ from both sides of the inequality.

$- t < 10 - 3$

Subtract $3$ from $10$ .

$- t < 7$

Step 3

Divide each term in $- t < 7$ by $- 1$ and simplify.

Divide each term in $- t < 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- t}{- 1} > \frac{7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{t}{1} > \frac{7}{- 1}$

Divide $t$ by $1$ .

$t > \frac{7}{- 1}$

Simplify the right side.

Divide $7$ by $- 1$ .

$t > - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$t > - 7$

Interval Notation:

$(- 7, \infty)$

Solve the Inequality for t 6t+3<7t+10

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