Algebra Examples

$f (2 x - 1) + f (x - 2) = 50$

Step 1

Simplify $f (2 x - 1) + f (x - 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$f (2 x) + f \cdot - 1 + f (x - 2) = 50$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 f x + f \cdot - 1 + f (x - 2) = 50$

Step 1.1.3

Move $- 1$ to the left of $f$ .

$2 f x - 1 \cdot f + f (x - 2) = 50$

Step 1.1.4

Rewrite $- 1 f$ as $- f$ .

$2 f x - f + f (x - 2) = 50$

Step 1.1.5

Apply the distributive property.

$2 f x - f + f x + f \cdot - 2 = 50$

Step 1.1.6

Move $- 2$ to the left of $f$ .

$2 f x - f + f x - 2 f = 50$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Add $2 f x$ and $f x$ .

$3 f x - f - 2 f = 50$

Step 1.2.2

Subtract $2 f$ from $- f$ .

$3 f x - 3 f = 50$

Step 2

Add $3 f$ to both sides of the equation.

$3 f x = 50 + 3 f$

Step 3

Divide each term in $3 f x = 50 + 3 f$ by $3 f$ and simplify.

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Step 3.1

Divide each term in $3 f x = 50 + 3 f$ by $3 f$ .

$\frac{3 f x}{3 f} = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 f x}{3 f} = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.2.1.2

Rewrite the expression.

$\frac{f x}{f} = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.2.2

Cancel the common factor of $f$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{f x}{f} = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $3$ .

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Step 3.3.1.1.1

Cancel the common factor.

$x = \frac{50}{3 f} + \frac{3 f}{3 f}$

Step 3.3.1.1.2

Rewrite the expression.

$x = \frac{50}{3 f} + \frac{f}{f}$

Step 3.3.1.2

Cancel the common factor of $f$ .

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Step 3.3.1.2.1

Cancel the common factor.

$x = \frac{50}{3 f} + \frac{f}{f}$

Step 3.3.1.2.2

Rewrite the expression.

$x = \frac{50}{3 f} + 1$