Linear Algebra Examples

$7 x - 5 = 4 y - 6$

Step 1

Rewrite the equation as $4 y - 6 = 7 x - 5$ .

$4 y - 6 = 7 x - 5$

Step 2

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

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Step 2.1

Add $6$ to both sides of the equation.

$4 y = 7 x - 5 + 6$

Step 2.2

Add $- 5$ and $6$ .

$4 y = 7 x + 1$

Step 3

Divide each term in $4 y = 7 x + 1$ by $4$ and simplify.

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Step 3.1

Divide each term in $4 y = 7 x + 1$ by $4$ .

$\frac{4 y}{4} = \frac{7 x}{4} + \frac{1}{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{7 x}{4} + \frac{1}{4}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{7 x}{4} + \frac{1}{4}$

Step 4

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 5