Solve the System of Inequalities 23<=4x-5 or 39<4x-5

$23 \leq 4 x - 5$ or $39 < 4 x - 5$

Step 1

Simplify the first inequality.

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

$4 x - 5 \geq 23$ or $39 < 4 x - 5$

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

Add $5$ to both sides of the inequality.

$4 x \geq 23 + 5$ or $39 < 4 x - 5$

Add $23$ and $5$ .

$4 x \geq 28$ or $39 < 4 x - 5$

Divide each term in $4 x \geq 28$ by $4$ and simplify.

Divide each term in $4 x \geq 28$ by $4$ .

$\frac{4 x}{4} \geq \frac{28}{4}$ or $39 < 4 x - 5$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{28}{4}$ or $39 < 4 x - 5$

Divide $x$ by $1$ .

$x \geq \frac{28}{4}$ or $39 < 4 x - 5$

Simplify the right side.

Divide $28$ by $4$ .

$x \geq 7$ or $39 < 4 x - 5$

Step 2

Simplify the second inequality.

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

$x \geq 7$ or $4 x - 5 > 39$

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

Add $5$ to both sides of the inequality.

$x \geq 7$ or $4 x > 39 + 5$

Add $39$ and $5$ .

$x \geq 7$ or $4 x > 44$

Divide each term in $4 x > 44$ by $4$ and simplify.

Divide each term in $4 x > 44$ by $4$ .

$x \geq 7$ or $\frac{4 x}{4} > \frac{44}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$x \geq 7$ or $\frac{4 x}{4} > \frac{44}{4}$

Divide $x$ by $1$ .

$x \geq 7$ or $x > \frac{44}{4}$

Simplify the right side.

Divide $44$ by $4$ .

$x \geq 7$ or $x > 11$

Step 3

The union consists of all of the elements that are contained in each interval.

$x \geq 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 7$

Interval Notation:

$[7, \infty)$

Step 5

Solve the System of Inequalities 23<=4x-5 or 39<4x-5

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