Algebra Examples

$8 - (- 2 t + 1) < t + 5 - 7$

Step 1

Simplify $8 - (- 2 t + 1)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$8 - (- 2 t) - 1 \cdot 1 < t + 5 - 7$

Step 1.1.2

Multiply $- 2$ by $- 1$ .

$8 + 2 t - 1 \cdot 1 < t + 5 - 7$

Step 1.1.3

Multiply $- 1$ by $1$ .

$8 + 2 t - 1 < t + 5 - 7$

Step 1.2

Subtract $1$ from $8$ .

$2 t + 7 < t + 5 - 7$

Step 2

Subtract $7$ from $5$ .

$2 t + 7 < t - 2$

Step 3

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

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Step 3.1

Subtract $t$ from both sides of the inequality.

$2 t + 7 - t < - 2$

Step 3.2

Subtract $t$ from $2 t$ .

$t + 7 < - 2$

Step 4

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

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Step 4.1

Subtract $7$ from both sides of the inequality.

$t < - 2 - 7$

Step 4.2

Subtract $7$ from $- 2$ .

$t < - 9$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$t < - 9$

Interval Notation:

$(- \infty, - 9)$