Pre-Algebra Examples Linear Equations and Inequalities

Solve for x

$5 - x > x + 1$

Step 1

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

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Step 1.1

Subtract $x$ from both sides of the inequality.

$5 - x - x > 1$

Step 1.2

Subtract $x$ from $- x$ .

$5 - 2 x > 1$

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.

$- 2 x > 1 - 5$

Step 2.2

Subtract $5$ from $1$ .

$- 2 x > - 4$

Step 3

Divide each term in $- 2 x > - 4$ by $- 2$ and simplify.

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Step 3.1

Divide each term in $- 2 x > - 4$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{- 4}{- 2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 4}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 4$ by $- 2$ .

$x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

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Solve for x

Linear Equations and Inequalities

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