Algebra Examples

$- \frac{1}{7} x + 200 > 0$

Step 1

Solve $x < 1400$ .

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Step 1.1

Combine $x$ and $\frac{1}{7}$ .

$- \frac{x}{7} + 200 > 0$

Step 1.2

Subtract $200$ from both sides of the inequality.

$- \frac{x}{7} > - 200$

Step 1.3

Divide each term in $- \frac{x}{7} > - 200$ by $- 1$ and simplify.

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Step 1.3.1

Divide each term in $- \frac{x}{7} > - 200$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{7}}{- 1} < \frac{- 200}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{x}{7}}{1} < \frac{- 200}{- 1}$

Step 1.3.2.2

Divide $\frac{x}{7}$ by $1$ .

$\frac{x}{7} < \frac{- 200}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Divide $- 200$ by $- 1$ .

$\frac{x}{7} < 200$

Step 1.4

Multiply both sides by $7$ .

$\frac{x}{7} \cdot 7 < 200 \cdot 7$

Step 1.5

Simplify.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Cancel the common factor of $7$ .

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Step 1.5.1.1.1

Cancel the common factor.

$\frac{x}{7} \cdot 7 < 200 \cdot 7$

Step 1.5.1.1.2

Rewrite the expression.

$x < 200 \cdot 7$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Multiply $200$ by $7$ .

$x < 1400$

Step 2

Use the inequality $x < 1400$ to build the set notation.

${x | x < 1400}$

Step 3