Algebra Examples

$5 x + 11 \geq - 9$ and $10 x - 3 \leq 27$

Step 1

Simplify the first inequality.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $11$ from both sides of the inequality.

$5 x \geq - 9 - 11$

Step 1.1.2

Subtract $11$ from $- 9$ .

$5 x \geq - 20$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{5 x}{5} \geq \frac{- 20}{5}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{- 20}{5}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{- 20}{5}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 20$ by $5$ .

$x \geq - 4$

Step 2

Simplify the second inequality.

Tap for more steps...

Step 2.1

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

Tap for more steps...

Step 2.1.1

Add $3$ to both sides of the inequality.

$10 x \leq 27 + 3$

Step 2.1.2

Add $27$ and $3$ .

$10 x \leq 30$

Step 2.2

Divide each term in $10 x \leq 30$ by $10$ and simplify.

Tap for more steps...

Step 2.2.1

Divide each term in $10 x \leq 30$ by $10$ .

$\frac{10 x}{10} \leq \frac{30}{10}$

Step 2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.1

Cancel the common factor of $10$ .

Tap for more steps...

Step 2.2.2.1.1

Cancel the common factor.

$\frac{10 x}{10} \leq \frac{30}{10}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{30}{10}$

Step 2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.3.1

Divide $30$ by $10$ .

$x \leq 3$

Step 3

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

$- 4 \leq x \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x \leq 3$

Interval Notation:

$[- 4, 3]$

Step 5