Solve the System of Inequalities 4<f+6 and f+6<5

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

Simplify the first inequality.

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

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

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

Subtract $6$ from both sides of the inequality.

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

Subtract $6$ from $4$ .

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

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

Subtract $6$ from both sides of the inequality.

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

Subtract $6$ from $5$ .

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

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

$- 2 < f < - 1$

The result can be shown in multiple forms.

Inequality Form:

$- 2 < f < - 1$

Interval Notation:

$(- 2, - 1)$