Pre-Algebra Examples

$1.7 t + 8 - 1.62 t < 0.4 t - 0.32 + 8$

Step 1

Subtract $1.62 t$ from $1.7 t$ .

$0.08 t + 8 < 0.4 t - 0.32 + 8$

Step 2

Add $- 0.32$ and $8$ .

$0.08 t + 8 < 0.4 t + 7.68$

Step 3

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

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Step 3.1

Subtract $0.4 t$ from both sides of the inequality.

$0.08 t + 8 - 0.4 t < 7.68$

Step 3.2

Subtract $0.4 t$ from $0.08 t$ .

$- 0.32 t + 8 < 7.68$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the inequality.

$- 0.32 t < 7.68 - 8$

Step 4.2

Subtract $8$ from $7.68$ .

$- 0.32 t < - 0.32$

Step 5

Divide each term in $- 0.32 t < - 0.32$ by $- 0.32$ and simplify.

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Step 5.1

Divide each term in $- 0.32 t < - 0.32$ by $- 0.32$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 0.32 t}{- 0.32} > \frac{- 0.32}{- 0.32}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 0.32$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 0.32 t}{- 0.32} > \frac{- 0.32}{- 0.32}$

Step 5.2.1.2

Divide $t$ by $1$ .

$t > \frac{- 0.32}{- 0.32}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 0.32$ by $- 0.32$ .

$t > 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$t > 1$

Interval Notation:

$(1, \infty)$