Basic Math Examples

$33 + 15 w = 3 w - w + 4 w$

Step 1

Since $w$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 w - w + 4 w = 33 + 15 w$

Step 2

Simplify $3 w - w + 4 w$ .

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Step 2.1

Subtract $w$ from $3 w$ .

$2 w + 4 w = 33 + 15 w$

Step 2.2

Add $2 w$ and $4 w$ .

$6 w = 33 + 15 w$

Step 3

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

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Step 3.1

Subtract $15 w$ from both sides of the equation.

$6 w - 15 w = 33$

Step 3.2

Subtract $15 w$ from $6 w$ .

$- 9 w = 33$

Step 4

Divide each term in $- 9 w = 33$ by $- 9$ and simplify.

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Step 4.1

Divide each term in $- 9 w = 33$ by $- 9$ .

$\frac{- 9 w}{- 9} = \frac{33}{- 9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 9 w}{- 9} = \frac{33}{- 9}$

Step 4.2.1.2

Divide $w$ by $1$ .

$w = \frac{33}{- 9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $33$ and $- 9$ .

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Step 4.3.1.1

Factor $3$ out of $33$ .

$w = \frac{3 (11)}{- 9}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $- 9$ .

$w = \frac{3 \cdot 11}{3 \cdot - 3}$

Step 4.3.1.2.2

Cancel the common factor.

$w = \frac{3 \cdot 11}{3 \cdot - 3}$

Step 4.3.1.2.3

Rewrite the expression.

$w = \frac{11}{- 3}$

Step 4.3.2

Move the negative in front of the fraction.

$w = - \frac{11}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{11}{3}$

Decimal Form:

$w = - 3.\overline{6}$

Mixed Number Form:

$w = - 3 \frac{2}{3}$