Algebra Examples

$3 x < 4 - 5 x < 5 + 3 x$

Step 1

Solve $3 x < 4 - 5 x$ for $x$ .

Tap for more steps...

Step 1.1

Move all terms containing $x$ to the left side of the inequality.

Tap for more steps...

Step 1.1.1

Add $5 x$ to both sides of the inequality.

$3 x + 5 x < 4$

Step 1.1.2

Add $3 x$ and $5 x$ .

$8 x < 4$

Step 1.2

Divide each term in $8 x < 4$ by $8$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $8 x < 4$ by $8$ .

$\frac{8 x}{8} < \frac{4}{8}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 x}{8} < \frac{4}{8}$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{4}{8}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Cancel the common factor of $4$ and $8$ .

Tap for more steps...

Step 1.2.3.1.1

Factor $4$ out of $4$ .

$x < \frac{4 (1)}{8}$

Step 1.2.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.3.1.2.1

Factor $4$ out of $8$ .

$x < \frac{4 \cdot 1}{4 \cdot 2}$

Step 1.2.3.1.2.2

Cancel the common factor.

$x < \frac{4 \cdot 1}{4 \cdot 2}$

Step 1.2.3.1.2.3

Rewrite the expression.

$x < \frac{1}{2}$

Step 2

Solve $4 - 5 x < 5 + 3 x$ for $x$ .

Tap for more steps...

Step 2.1

Move all terms containing $x$ to the left side of the inequality.

Tap for more steps...

Step 2.1.1

Subtract $3 x$ from both sides of the inequality.

$4 - 5 x - 3 x < 5$

Step 2.1.2

Subtract $3 x$ from $- 5 x$ .

$4 - 8 x < 5$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $4$ from both sides of the inequality.

$- 8 x < 5 - 4$

Step 2.2.2

Subtract $4$ from $5$ .

$- 8 x < 1$

Step 2.3

Divide each term in $- 8 x < 1$ by $- 8$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- 8 x < 1$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{1}{- 8}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of $- 8$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{1}{- 8}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{- 8}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Move the negative in front of the fraction.

$x > - \frac{1}{8}$

Step 3

Find the intersection of $x < \frac{1}{2}$ and $x > - \frac{1}{8}$ .

$- \frac{1}{8} < x < \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{1}{8} < x < \frac{1}{2}$

Interval Notation:

$(- \frac{1}{8}, \frac{1}{2})$

Step 5