Pre-Algebra Examples

$w - \frac{10}{4} > \frac{5 w}{8}$

Step 1

Multiply both sides by $8$ .

$(w - \frac{10}{4}) \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $(w - \frac{10}{4}) \cdot 8$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor of $10$ and $4$ .

Tap for more steps...

Step 2.1.1.1.1

Factor $2$ out of $10$ .

$(w - \frac{2 (5)}{4}) \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.1.2

Cancel the common factors.

Tap for more steps...

Step 2.1.1.1.2.1

Factor $2$ out of $4$ .

$(w - \frac{2 \cdot 5}{2 \cdot 2}) \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.1.2.2

Cancel the common factor.

$(w - \frac{2 \cdot 5}{2 \cdot 2}) \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.1.2.3

Rewrite the expression.

$(w - \frac{5}{2}) \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.2

Apply the distributive property.

$w \cdot 8 - \frac{5}{2} \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.3

Move $8$ to the left of $w$ .

$8 \cdot w - \frac{5}{2} \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.4.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$8 \cdot w + \frac{- 5}{2} \cdot 8 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.4.2

Factor $2$ out of $8$ .

$8 \cdot w + \frac{- 5}{2} \cdot (2 (4)) > \frac{5 w}{8} \cdot 8$

Step 2.1.1.4.3

Cancel the common factor.

$8 \cdot w + \frac{- 5}{2} \cdot (2 \cdot 4) > \frac{5 w}{8} \cdot 8$

Step 2.1.1.4.4

Rewrite the expression.

$8 \cdot w - 5 \cdot 4 > \frac{5 w}{8} \cdot 8$

Step 2.1.1.5

Multiply $- 5$ by $4$ .

$8 w - 20 > \frac{5 w}{8} \cdot 8$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$8 w - 20 > \frac{5 w}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$8 w - 20 > 5 w$

Step 3

Solve for $w$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $5 w$ from both sides of the inequality.

$8 w - 20 - 5 w > 0$

Step 3.1.2

Subtract $5 w$ from $8 w$ .

$3 w - 20 > 0$

Step 3.2

Add $20$ to both sides of the inequality.

$3 w > 20$

Step 3.3

Divide each term in $3 w > 20$ by $3$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $3 w > 20$ by $3$ .

$\frac{3 w}{3} > \frac{20}{3}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.2.1.1

Cancel the common factor.

$\frac{3 w}{3} > \frac{20}{3}$

Step 3.3.2.1.2

Divide $w$ by $1$ .

$w > \frac{20}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$w > \frac{20}{3}$

Interval Notation:

$(\frac{20}{3}, \infty)$