Algebra Examples

$y = 4 x - 5$ and $y = a x + 2$

Step 1

Solve the equation for $x$ .

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Step 1.1

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

$4 x - 5 - a x = 2$

$y = 4 x - 5$

Step 1.2

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

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Step 1.2.1

Add $5$ to both sides of the equation.

$4 x - a x = 2 + 5$

$y = 4 x - 5$

Step 1.2.2

Add $2$ and $5$ .

$4 x - a x = 7$

$y = 4 x - 5$

$4 x - a x = 7$

$y = 4 x - 5$

Step 1.3

Factor $x$ out of $4 x - a x$ .

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Step 1.3.1

Factor $x$ out of $4 x$ .

$x \cdot 4 - a x = 7$

$y = 4 x - 5$

Step 1.3.2

Factor $x$ out of $- a x$ .

$x \cdot 4 + x (- a) = 7$

$y = 4 x - 5$

Step 1.3.3

Factor $x$ out of $x \cdot 4 + x (- a)$ .

$x \cdot (4 - a) = 7$

$y = 4 x - 5$

Step 1.3.4

Multiply $x$ by $4 - a$ .

$x (4 - a) = 7$

$y = 4 x - 5$

$x (4 - a) = 7$

$y = 4 x - 5$

Step 1.4

Divide each term in $x (4 - a) = 7$ by $4 - a$ and simplify.

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Step 1.4.1

Divide each term in $x (4 - a) = 7$ by $4 - a$ .

$\frac{x (4 - a)}{4 - a} = \frac{7}{4 - a}$

$y = 4 x - 5$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $4 - a$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{x (4 - a)}{4 - a} = \frac{7}{4 - a}$

$y = 4 x - 5$

Step 1.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{4 - a}$

$y = 4 x - 5$

$x = \frac{7}{4 - a}$

$y = 4 x - 5$

$x = \frac{7}{4 - a}$

$y = 4 x - 5$

$x = \frac{7}{4 - a}$

$y = 4 x - 5$

$x = \frac{7}{4 - a}$

$y = 4 x - 5$

Step 2

Simplify the right side.

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Step 2.1

Simplify $4 (\frac{7}{4 - a}) - 5$ .

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Step 2.1.1

Multiply $4 (\frac{7}{4 - a})$ .

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Step 2.1.1.1

Combine $4$ and $\frac{7}{4 - a}$ .

$y = \frac{4 \cdot 7}{4 - a} - 5$

$x = \frac{7}{4 - a}$

Step 2.1.1.2

Multiply $4$ by $7$ .

$y = \frac{28}{4 - a} - 5$

$x = \frac{7}{4 - a}$

$y = \frac{28}{4 - a} - 5$

$x = \frac{7}{4 - a}$

Step 2.1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{4 - a}{4 - a}$ .

$y = \frac{28}{4 - a} - 5 \cdot \frac{4 - a}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.3

Simplify terms.

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Step 2.1.3.1

Combine $- 5$ and $\frac{4 - a}{4 - a}$ .

$y = \frac{28}{4 - a} + \frac{- 5 (4 - a)}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.3.2

Combine the numerators over the common denominator.

$y = \frac{28 - 5 (4 - a)}{4 - a}$

$x = \frac{7}{4 - a}$

$y = \frac{28 - 5 (4 - a)}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.4

Simplify the numerator.

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Step 2.1.4.1

Apply the distributive property.

$y = \frac{28 - 5 \cdot 4 - 5 (- a)}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.4.2

Multiply $- 5$ by $4$ .

$y = \frac{28 - 20 - 5 (- a)}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.4.3

Multiply $- 1$ by $- 5$ .

$y = \frac{28 - 20 + 5 a}{4 - a}$

$x = \frac{7}{4 - a}$

Step 2.1.4.4

Subtract $20$ from $28$ .

$y = \frac{8 + 5 a}{4 - a}$

$x = \frac{7}{4 - a}$

$y = \frac{8 + 5 a}{4 - a}$

$x = \frac{7}{4 - a}$

$y = \frac{8 + 5 a}{4 - a}$

$x = \frac{7}{4 - a}$

$y = \frac{8 + 5 a}{4 - a}$

$x = \frac{7}{4 - a}$