Algebra Examples

$f (x) = 2 x + 11$ and $g (x) = - 3 x - 22$

Step 1

Substitute $- 3 x - 22$ for $f (x)$ .

$- 3 x - 22 = 2 x + 11$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

Subtract $2 x$ from both sides of the equation.

$- 3 x - 22 - 2 x = 11$

Step 2.1.2

Subtract $2 x$ from $- 3 x$ .

$- 5 x - 22 = 11$

Step 2.2

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

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Step 2.2.1

Add $22$ to both sides of the equation.

$- 5 x = 11 + 22$

Step 2.2.2

Add $11$ and $22$ .

$- 5 x = 33$

Step 2.3

Divide each term in $- 5 x = 33$ by $- 5$ and simplify.

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Step 2.3.1

Divide each term in $- 5 x = 33$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{33}{- 5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{33}{- 5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{33}{- 5}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$x = - \frac{33}{5}$