Trigonometry Examples

$8 x + 5 < 5 x + 3$

Step 1

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

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Step 1.1

Subtract $5 x$ from both sides of the inequality.

$8 x + 5 - 5 x < 3$

Step 1.2

Subtract $5 x$ from $8 x$ .

$3 x + 5 < 3$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the inequality.

$3 x < 3 - 5$

Step 2.2

Subtract $5$ from $3$ .

$3 x < - 2$

Step 3

Divide each term in $3 x < - 2$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x < - 2$ by $3$ .

$\frac{3 x}{3} < \frac{- 2}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} < \frac{- 2}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 2}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x < - \frac{2}{3}$

Step 4

Convert the inequality to interval notation.

$(- \infty, - \frac{2}{3})$

Step 5