Algebra Examples

$3 (2 x - 1) > 4 + 5 (X - 1)$

Step 1

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

$4 + 5 (X - 1) < 3 (2 x - 1)$

Step 2

Simplify $4 + 5 (X - 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$4 + 5 X + 5 \cdot - 1 < 3 (2 x - 1)$

Step 2.1.2

Multiply $5$ by $- 1$ .

$4 + 5 X - 5 < 3 (2 x - 1)$

Step 2.2

Subtract $5$ from $4$ .

$5 X - 1 < 3 (2 x - 1)$

Step 3

Simplify $3 (2 x - 1)$ .

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Step 3.1

Apply the distributive property.

$5 X - 1 < 3 (2 x) + 3 \cdot - 1$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $2$ by $3$ .

$5 X - 1 < 6 x + 3 \cdot - 1$

Step 3.2.2

Multiply $3$ by $- 1$ .

$5 X - 1 < 6 x - 3$

Step 4

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

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Step 4.1

Add $1$ to both sides of the inequality.

$5 X < 6 x - 3 + 1$

Step 4.2

Add $- 3$ and $1$ .

$5 X < 6 x - 2$

Step 5

Divide each term in $5 X < 6 x - 2$ by $5$ and simplify.

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Step 5.1

Divide each term in $5 X < 6 x - 2$ by $5$ .

$\frac{5 X}{5} < \frac{6 x}{5} + \frac{- 2}{5}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $5$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{5 X}{5} < \frac{6 x}{5} + \frac{- 2}{5}$

Step 5.2.1.2

Divide $X$ by $1$ .

$X < \frac{6 x}{5} + \frac{- 2}{5}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Move the negative in front of the fraction.

$X < \frac{6 x}{5} - \frac{2}{5}$