Solve the System of Inequalities 17>3x+5 or 26<=3x+5

$17 > 3 x + 5$ or $26 \leq 3 x + 5$

Step 1

Simplify the first inequality.

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

$3 x + 5 < 17$ or $26 \leq 3 x + 5$

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

Subtract $5$ from both sides of the inequality.

$3 x < 17 - 5$ or $26 \leq 3 x + 5$

Subtract $5$ from $17$ .

$3 x < 12$ or $26 \leq 3 x + 5$

Divide each term in $3 x < 12$ by $3$ and simplify.

Divide each term in $3 x < 12$ by $3$ .

$\frac{3 x}{3} < \frac{12}{3}$ or $26 \leq 3 x + 5$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{12}{3}$ or $26 \leq 3 x + 5$

Divide $x$ by $1$ .

$x < \frac{12}{3}$ or $26 \leq 3 x + 5$

Simplify the right side.

Divide $12$ by $3$ .

$x < 4$ or $26 \leq 3 x + 5$

Step 2

Simplify the second inequality.

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

$x < 4$ or $3 x + 5 \geq 26$

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

Subtract $5$ from both sides of the inequality.

$x < 4$ or $3 x \geq 26 - 5$

Subtract $5$ from $26$ .

$x < 4$ or $3 x \geq 21$

Divide each term in $3 x \geq 21$ by $3$ and simplify.

Divide each term in $3 x \geq 21$ by $3$ .

$x < 4$ or $\frac{3 x}{3} \geq \frac{21}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$x < 4$ or $\frac{3 x}{3} \geq \frac{21}{3}$

Divide $x$ by $1$ .

$x < 4$ or $x \geq \frac{21}{3}$

Simplify the right side.

Divide $21$ by $3$ .

$x < 4$ or $x \geq 7$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 4 or x \geq 7$

Interval Notation:

$(- \infty, 4) \cup [7, \infty)$

Step 4

Solve the System of Inequalities 17>3x+5 or 26<=3x+5

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