Algebra Examples

$- 4 + b x = 2 x + 3 (x + 1)$

Step 1

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

$2 x + 3 (x + 1) = - 4 + b x$

Step 2

Simplify $2 x + 3 (x + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 x + 3 x + 3 \cdot 1 = - 4 + b x$

Step 2.1.2

Multiply $3$ by $1$ .

$2 x + 3 x + 3 = - 4 + b x$

Step 2.2

Add $2 x$ and $3 x$ .

$5 x + 3 = - 4 + b x$

Step 3

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

$5 x + 3 - b x = - 4$

Step 4

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

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Step 4.1

Subtract $3$ from both sides of the equation.

$5 x - b x = - 4 - 3$

Step 4.2

Subtract $3$ from $- 4$ .

$5 x - b x = - 7$

Step 5

Factor $x$ out of $5 x - b x$ .

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Step 5.1

Factor $x$ out of $5 x$ .

$x \cdot 5 - b x = - 7$

Step 5.2

Factor $x$ out of $- b x$ .

$x \cdot 5 + x (- b) = - 7$

Step 5.3

Factor $x$ out of $x \cdot 5 + x (- b)$ .

$x (5 - b) = - 7$

Step 6

Divide each term in $x (5 - b) = - 7$ by $5 - b$ and simplify.

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Step 6.1

Divide each term in $x (5 - b) = - 7$ by $5 - b$ .

$\frac{x (5 - b)}{5 - b} = \frac{- 7}{5 - b}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5 - b$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{x (5 - b)}{5 - b} = \frac{- 7}{5 - b}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7}{5 - b}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$x = - \frac{7}{5 - b}$

Step 7

To rewrite as a function of $b$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $b$ is on the other side.

$f (b) = - \frac{7}{5 - b}$