Algebra Examples

$9.1 g + 4.5 < 10.1 g$

Step 1

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

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Step 1.1

Subtract $10.1 g$ from both sides of the inequality.

$9.1 g + 4.5 - 10.1 g < 0$

Step 1.2

Subtract $10.1 g$ from $9.1 g$ .

$- 1 g + 4.5 < 0$

Step 2

Subtract $4.5$ from both sides of the inequality.

$- 1 g < - 4.5$

Step 3

Divide each term in $- 1 g < - 4.5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- 1 g < - 4.5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 1 g}{- 1} > \frac{- 4.5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 1$ .

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Step 3.2.1.1

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{- 1 (1) g}{- 1} > \frac{- 4.5}{- 1}$

Step 3.2.1.2

Factor $1$ out of $- 1 (1) g$ .

$\frac{1 (- 1 \cdot 1 g)}{- 1} > \frac{- 4.5}{- 1}$

Step 3.2.1.3

Move the negative one from the denominator of $\frac{- 1 \cdot 1 g}{- 1}$ .

$- 1 \cdot (- 1 \cdot 1 g) > \frac{- 4.5}{- 1}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Rewrite $- 1 \cdot (- 1 \cdot 1 g)$ as $- (- 1 \cdot 1 g)$ .

$- (- 1 \cdot 1 g) > \frac{- 4.5}{- 1}$

Step 3.2.2.2

Multiply $- 1$ by $1$ .

$- (- 1 g) > \frac{- 4.5}{- 1}$

Step 3.2.2.3

Rewrite $- 1 g$ as $- g$ .

$- - g > \frac{- 4.5}{- 1}$

Step 3.2.3

Multiply $- - g$ .

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Step 3.2.3.1

Multiply $- 1$ by $- 1$ .

$1 g > \frac{- 4.5}{- 1}$

Step 3.2.3.2

Multiply $g$ by $1$ .

$g > \frac{- 4.5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 4.5$ by $- 1$ .

$g > 4.5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$g > 4.5$

Interval Notation:

$(4.5, \infty)$