Solve the System of Inequalities 5x-3>=17 or 5x-3>27

$5 x - 3 \geq 17$ or $5 x - 3 > 27$

Step 1

Simplify the first inequality.

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

Add $3$ to both sides of the inequality.

$5 x \geq 17 + 3$ or $5 x - 3 > 27$

Add $17$ and $3$ .

$5 x \geq 20$ or $5 x - 3 > 27$

Divide each term in $5 x \geq 20$ by $5$ and simplify.

Divide each term in $5 x \geq 20$ by $5$ .

$\frac{5 x}{5} \geq \frac{20}{5}$ or $5 x - 3 > 27$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{20}{5}$ or $5 x - 3 > 27$

Divide $x$ by $1$ .

$x \geq \frac{20}{5}$ or $5 x - 3 > 27$

Simplify the right side.

Divide $20$ by $5$ .

$x \geq 4$ or $5 x - 3 > 27$

Step 2

Simplify the second inequality.

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

Add $3$ to both sides of the inequality.

$x \geq 4$ or $5 x > 27 + 3$

Add $27$ and $3$ .

$x \geq 4$ or $5 x > 30$

Divide each term in $5 x > 30$ by $5$ and simplify.

Divide each term in $5 x > 30$ by $5$ .

$x \geq 4$ or $\frac{5 x}{5} > \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$x \geq 4$ or $\frac{5 x}{5} > \frac{30}{5}$

Divide $x$ by $1$ .

$x \geq 4$ or $x > \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x \geq 4$ or $x > 6$

Step 3

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

$x \geq 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 4$

Interval Notation:

$[4, \infty)$

Step 5

Solve the System of Inequalities 5x-3>=17 or 5x-3>27

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