Pre-Algebra Examples

$4 x - 4 - 3 x > 13 - 7 x - 1 + 8$

Step 1

Subtract $3 x$ from $4 x$ .

$x - 4 > 13 - 7 x - 1 + 8$

Step 2

Simplify $13 - 7 x - 1 + 8$ .

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Step 2.1

Subtract $1$ from $13$ .

$x - 4 > - 7 x + 12 + 8$

Step 2.2

Add $12$ and $8$ .

$x - 4 > - 7 x + 20$

Step 3

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

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Step 3.1

Add $7 x$ to both sides of the inequality.

$x - 4 + 7 x > 20$

Step 3.2

Add $x$ and $7 x$ .

$8 x - 4 > 20$

Step 4

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

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Step 4.1

Add $4$ to both sides of the inequality.

$8 x > 20 + 4$

Step 4.2

Add $20$ and $4$ .

$8 x > 24$

Step 5

Divide each term in $8 x > 24$ by $8$ and simplify.

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Step 5.1

Divide each term in $8 x > 24$ by $8$ .

$\frac{8 x}{8} > \frac{24}{8}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $8$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{8 x}{8} > \frac{24}{8}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x > \frac{24}{8}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $24$ by $8$ .

$x > 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > 3$

Interval Notation:

$(3, \infty)$