Algebra Examples

$4 < f + 6$ and $f + 6 < 5$

Step 1

Simplify the first inequality.

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Step 1.1

Rewrite so $f$ is on the left side of the inequality.

$f + 6 > 4$ and $f + 6 < 5$

Step 1.2

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

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Step 1.2.1

Subtract $6$ from both sides of the inequality.

$f > 4 - 6$ and $f + 6 < 5$

Step 1.2.2

Subtract $6$ from $4$ .

$f > - 2$ and $f + 6 < 5$

Step 2

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

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Step 2.1

Subtract $6$ from both sides of the inequality.

$f > - 2$ and $f < 5 - 6$

Step 2.2

Subtract $6$ from $5$ .

$f > - 2$ and $f < - 1$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 2 < f < - 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 2 < f < - 1$

Interval Notation:

$(- 2, - 1)$

Step 5