Algebra Examples

$- 4 x + 2 y = - 7$

Step 1

Add $4 x$ to both sides of the equation.

$2 y = - 7 + 4 x$

Step 2

Divide each term in $2 y = - 7 + 4 x$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = - 7 + 4 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 7}{2} + \frac{4 x}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 7}{2} + \frac{4 x}{2}$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{2} + \frac{4 x}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{2} + \frac{4 x}{2}$

Step 2.3.1.2

Cancel the common factor of $4$ and $2$ .

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Step 2.3.1.2.1

Factor $2$ out of $4 x$ .

$y = - \frac{7}{2} + \frac{2 (2 x)}{2}$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $2$ .

$y = - \frac{7}{2} + \frac{2 (2 x)}{2 (1)}$

Step 2.3.1.2.2.2

Cancel the common factor.

$y = - \frac{7}{2} + \frac{2 (2 x)}{2 \cdot 1}$

Step 2.3.1.2.2.3

Rewrite the expression.

$y = - \frac{7}{2} + \frac{2 x}{1}$

Step 2.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - \frac{7}{2} + 2 x$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 5

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \infty, \infty), {y | y \in ℝ}$

Step 6