Algebra Examples

$- 7 x > 6 (- 5 x - \frac{1}{2}) - 3$

Step 1

Simplify $6 (- 5 x - \frac{1}{2}) - 3$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 7 x > 6 (- 5 x) + 6 (- \frac{1}{2}) - 3$

Step 1.1.2

Multiply $- 5$ by $6$ .

$- 7 x > - 30 x + 6 (- \frac{1}{2}) - 3$

Step 1.1.3

Cancel the common factor of $2$ .

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Step 1.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 7 x > - 30 x + 6 (\frac{- 1}{2}) - 3$

Step 1.1.3.2

Factor $2$ out of $6$ .

$- 7 x > - 30 x + 2 (3) \frac{- 1}{2} - 3$

Step 1.1.3.3

Cancel the common factor.

$- 7 x > - 30 x + 2 \cdot 3 \frac{- 1}{2} - 3$

Step 1.1.3.4

Rewrite the expression.

$- 7 x > - 30 x + 3 \cdot - 1 - 3$

Step 1.1.4

Multiply $3$ by $- 1$ .

$- 7 x > - 30 x - 3 - 3$

Step 1.2

Subtract $3$ from $- 3$ .

$- 7 x > - 30 x - 6$

Step 2

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

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Step 2.1

Add $30 x$ to both sides of the inequality.

$- 7 x + 30 x > - 6$

Step 2.2

Add $- 7 x$ and $30 x$ .

$23 x > - 6$

Step 3

Divide each term in $23 x > - 6$ by $23$ and simplify.

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Step 3.1

Divide each term in $23 x > - 6$ by $23$ .

$\frac{23 x}{23} > \frac{- 6}{23}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $23$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{23 x}{23} > \frac{- 6}{23}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 6}{23}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$x > - \frac{6}{23}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{6}{23}$

Interval Notation:

$(- \frac{6}{23}, \infty)$