Pre-Algebra Examples

$- \frac{2}{7} w + 2 w = \frac{1}{2} w + \frac{17}{2}$

Step 1

Simplify $- \frac{2}{7} w + 2 w$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $w$ and $\frac{2}{7}$ .

$- \frac{w \cdot 2}{7} + 2 w = \frac{1}{2} w + \frac{17}{2}$

Step 1.1.2

Move $2$ to the left of $w$ .

$- \frac{2 w}{7} + 2 w = \frac{1}{2} w + \frac{17}{2}$

Step 1.2

To write $2 w$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{2 w}{7} + 2 w \cdot \frac{7}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $2 w$ and $\frac{7}{7}$ .

$- \frac{2 w}{7} + \frac{2 w \cdot 7}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{- 2 w + 2 w \cdot 7}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Factor $2 w$ out of $- 2 w + 2 w \cdot 7$ .

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Step 1.4.1.1

Factor $2 w$ out of $- 2 w$ .

$\frac{2 w (- 1) + 2 w \cdot 7}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.4.1.2

Factor $2 w$ out of $2 w \cdot 7$ .

$\frac{2 w (- 1) + 2 w (7)}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.4.1.3

Factor $2 w$ out of $2 w (- 1) + 2 w (7)$ .

$\frac{2 w (- 1 + 7)}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.4.2

Add $- 1$ and $7$ .

$\frac{2 w \cdot 6}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 1.4.3

Multiply $6$ by $2$ .

$\frac{12 w}{7} = \frac{1}{2} w + \frac{17}{2}$

Step 2

Combine $\frac{1}{2}$ and $w$ .

$\frac{12 w}{7} = \frac{w}{2} + \frac{17}{2}$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$w = 7$

Step 4