Solve the System of Inequalities 2x+5<23 and 27>=2x+5

$2 x + 5 < 23$ and $27 \geq 2 x + 5$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$2 x < 23 - 5$ and $27 \geq 2 x + 5$

Subtract $5$ from $23$ .

$2 x < 18$ and $27 \geq 2 x + 5$

Divide each term in $2 x < 18$ by $2$ and simplify.

Divide each term in $2 x < 18$ by $2$ .

$\frac{2 x}{2} < \frac{18}{2}$ and $27 \geq 2 x + 5$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{18}{2}$ and $27 \geq 2 x + 5$

Divide $x$ by $1$ .

$x < \frac{18}{2}$ and $27 \geq 2 x + 5$

Simplify the right side.

Divide $18$ by $2$ .

$x < 9$ and $27 \geq 2 x + 5$

Step 2

Simplify the second inequality.

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

$x < 9$ and $2 x + 5 \leq 27$

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

Subtract $5$ from both sides of the inequality.

$x < 9$ and $2 x \leq 27 - 5$

Subtract $5$ from $27$ .

$x < 9$ and $2 x \leq 22$

Divide each term in $2 x \leq 22$ by $2$ and simplify.

Divide each term in $2 x \leq 22$ by $2$ .

$x < 9$ and $\frac{2 x}{2} \leq \frac{22}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$x < 9$ and $\frac{2 x}{2} \leq \frac{22}{2}$

Divide $x$ by $1$ .

$x < 9$ and $x \leq \frac{22}{2}$

Simplify the right side.

Divide $22$ by $2$ .

$x < 9$ and $x \leq 11$

Step 3

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

$x < 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 9$

Interval Notation:

$(- \infty, 9)$

Step 5

Solve the System of Inequalities 2x+5<23 and 27>=2x+5

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