Pre-Algebra Examples

$7 x - 14 + x > - 32 + 4 x$

Step 1

Add $7 x$ and $x$ .

$8 x - 14 > - 32 + 4 x$

Step 2

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

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Step 2.1

Subtract $4 x$ from both sides of the inequality.

$8 x - 14 - 4 x > - 32$

Step 2.2

Subtract $4 x$ from $8 x$ .

$4 x - 14 > - 32$

Step 3

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

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Step 3.1

Add $14$ to both sides of the inequality.

$4 x > - 32 + 14$

Step 3.2

Add $- 32$ and $14$ .

$4 x > - 18$

Step 4

Divide each term in $4 x > - 18$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x > - 18$ by $4$ .

$\frac{4 x}{4} > \frac{- 18}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} > \frac{- 18}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 18}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $- 18$ and $4$ .

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Step 4.3.1.1

Factor $2$ out of $- 18$ .

$x > \frac{2 (- 9)}{4}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $4$ .

$x > \frac{2 \cdot - 9}{2 \cdot 2}$

Step 4.3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot - 9}{2 \cdot 2}$

Step 4.3.1.2.3

Rewrite the expression.

$x > \frac{- 9}{2}$

Step 4.3.2

Move the negative in front of the fraction.

$x > - \frac{9}{2}$

Step 5