Pre-Algebra Examples

$4 (x - 4) < 8$ , $x + 7 > 8$

Step 1

Solve $4 (x - 4) < 8$ for $x$ .

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Step 1.1

Divide each term in $4 (x - 4) < 8$ by $4$ and simplify.

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Step 1.1.1

Divide each term in $4 (x - 4) < 8$ by $4$ .

$\frac{4 (x - 4)}{4} < \frac{8}{4}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $4$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{4 (x - 4)}{4} < \frac{8}{4}$

Step 1.1.2.1.2

Divide $x - 4$ by $1$ .

$x - 4 < \frac{8}{4}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Divide $8$ by $4$ .

$x - 4 < 2$

Step 1.2

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

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Step 1.2.1

Add $4$ to both sides of the inequality.

$x < 2 + 4$

Step 1.2.2

Add $2$ and $4$ .

$x < 6$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the inequality.

$x > 8 - 7$

Step 2.2

Subtract $7$ from $8$ .

$x > 1$

Step 3

Find the intersection of $x < 6$ and $x > 1$ .

$1 < x < 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 6$

Interval Notation:

$(1, 6)$

Step 5