Algebra Examples

$8 \leq x + 5$ and $16 > x + 5$

Step 1

Simplify the first inequality.

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Step 1.1

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

$x + 5 \geq 8$ and $16 > x + 5$

Step 1.2

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

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Step 1.2.1

Subtract $5$ from both sides of the inequality.

$x \geq 8 - 5$ and $16 > x + 5$

Step 1.2.2

Subtract $5$ from $8$ .

$x \geq 3$ and $16 > x + 5$

Step 2

Simplify the second inequality.

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Step 2.1

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

$x \geq 3$ and $x + 5 < 16$

Step 2.2

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

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Step 2.2.1

Subtract $5$ from both sides of the inequality.

$x \geq 3$ and $x < 16 - 5$

Step 2.2.2

Subtract $5$ from $16$ .

$x \geq 3$ and $x < 11$

Step 3

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

$3 \leq x < 11$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$3 \leq x < 11$

Interval Notation:

$[3, 11)$

Step 5