Algebra Examples

$7 + t \leq 2 (t + 3) + 2$

Step 1

Simplify $2 (t + 3) + 2$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$7 + t \leq 2 t + 2 \cdot 3 + 2$

Step 1.1.2

Multiply $2$ by $3$ .

$7 + t \leq 2 t + 6 + 2$

Step 1.2

Add $6$ and $2$ .

$7 + t \leq 2 t + 8$

Step 2

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

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Step 2.1

Subtract $2 t$ from both sides of the inequality.

$7 + t - 2 t \leq 8$

Step 2.2

Subtract $2 t$ from $t$ .

$7 - t \leq 8$

Step 3

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

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Step 3.1

Subtract $7$ from both sides of the inequality.

$- t \leq 8 - 7$

Step 3.2

Subtract $7$ from $8$ .

$- t \leq 1$

Step 4

Divide each term in $- t \leq 1$ by $- 1$ and simplify.

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Step 4.1

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

$\frac{- t}{- 1} \geq \frac{1}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{t}{1} \geq \frac{1}{- 1}$

Step 4.2.2

Divide $t$ by $1$ .

$t \geq \frac{1}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $1$ by $- 1$ .

$t \geq - 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$t \geq - 1$

Interval Notation:

$[- 1, \infty)$