Algebra Examples

$2 x + y = 3$ $y = \frac{1}{2} x - \frac{9}{2}$

Step 1

Subtract $2 x$ from both sides of the equation.

$y = 3 - 2 x$

$y = \frac{1}{2} x - \frac{9}{2}$

Step 2

Replace all occurrences of $y$ with $3 - 2 x$ in each equation.

Tap for more steps...

Step 2.1

Replace all occurrences of $y$ in $y = 3 - 2 x$ with $3 - 2 x$ .

$3 - 2 x = 3 - 2 x$

$y = \frac{1}{2} x - \frac{9}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$3 - 2 x = 3 - 2 x$

$y = \frac{1}{2} x - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

$y = \frac{1}{2} x - \frac{9}{2}$

Step 2.3

Replace all occurrences of $y$ in $y = \frac{1}{2} x - \frac{9}{2}$ with $3 - 2 x$ .

$3 - 2 x = \frac{1}{2} x - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

Step 2.4

Simplify $3 - 2 x = \frac{1}{2} x - \frac{9}{2}$ .

Tap for more steps...

Step 2.4.1

Simplify the left side.

Tap for more steps...

Step 2.4.1.1

Remove parentheses.

$3 - 2 x = \frac{1}{2} x - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

$3 - 2 x = \frac{1}{2} x - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

Step 2.4.2

Simplify the right side.

Tap for more steps...

Step 2.4.2.1

Combine $\frac{1}{2}$ and $x$ .

$3 - 2 x = \frac{x}{2} - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

$3 - 2 x = \frac{x}{2} - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

$3 - 2 x = \frac{x}{2} - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

$3 - 2 x = \frac{x}{2} - \frac{9}{2}$

$3 - 2 x = 3 - 2 x$

Step 3

Remove any equations from the system that are always true.

$3 - 2 x = \frac{x}{2} - \frac{9}{2}$

Step 4

Solve for $x$ in $3 - 2 x = \frac{x}{2} - \frac{9}{2}$ .

Tap for more steps...

Step 4.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 4.1.1

Subtract $\frac{x}{2}$ from both sides of the equation.

$3 - 2 x - \frac{x}{2} = - \frac{9}{2}$

Step 4.1.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 - 2 x \cdot \frac{2}{2} - \frac{x}{2} = - \frac{9}{2}$

Step 4.1.3

Combine $- 2 x$ and $\frac{2}{2}$ .

$3 + \frac{- 2 x \cdot 2}{2} - \frac{x}{2} = - \frac{9}{2}$

Step 4.1.4

Combine the numerators over the common denominator.

$3 + \frac{- 2 x \cdot 2 - x}{2} = - \frac{9}{2}$

Step 4.1.5

Simplify each term.

Tap for more steps...

Step 4.1.5.1

Simplify the numerator.

Tap for more steps...

Step 4.1.5.1.1

Factor $x$ out of $- 2 x \cdot 2 - x$ .

Tap for more steps...

Step 4.1.5.1.1.1

Factor $x$ out of $- 2 x \cdot 2$ .

$3 + \frac{x (- 2 \cdot 2) - x}{2} = - \frac{9}{2}$

Step 4.1.5.1.1.2

Factor $x$ out of $- x$ .

$3 + \frac{x (- 2 \cdot 2) + x \cdot - 1}{2} = - \frac{9}{2}$

Step 4.1.5.1.1.3

Factor $x$ out of $x (- 2 \cdot 2) + x \cdot - 1$ .

$3 + \frac{x (- 2 \cdot 2 - 1)}{2} = - \frac{9}{2}$

$3 + \frac{x (- 2 \cdot 2 - 1)}{2} = - \frac{9}{2}$

Step 4.1.5.1.2

Multiply $- 2$ by $2$ .

$3 + \frac{x (- 4 - 1)}{2} = - \frac{9}{2}$

Step 4.1.5.1.3

Subtract $1$ from $- 4$ .

$3 + \frac{x \cdot - 5}{2} = - \frac{9}{2}$

$3 + \frac{x \cdot - 5}{2} = - \frac{9}{2}$

Step 4.1.5.2

Move $- 5$ to the left of $x$ .

$3 + \frac{- 5 \cdot x}{2} = - \frac{9}{2}$

Step 4.1.5.3

Move the negative in front of the fraction.

$3 - \frac{5 x}{2} = - \frac{9}{2}$

$3 - \frac{5 x}{2} = - \frac{9}{2}$

$3 - \frac{5 x}{2} = - \frac{9}{2}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $3$ from both sides of the equation.

$- \frac{5 x}{2} = - \frac{9}{2} - 3$

Step 4.2.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 x}{2} = - \frac{9}{2} - 3 \cdot \frac{2}{2}$

Step 4.2.3

Combine $- 3$ and $\frac{2}{2}$ .

$- \frac{5 x}{2} = - \frac{9}{2} + \frac{- 3 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$- \frac{5 x}{2} = \frac{- 9 - 3 \cdot 2}{2}$

Step 4.2.5

Simplify the numerator.

Tap for more steps...

Step 4.2.5.1

Multiply $- 3$ by $2$ .

$- \frac{5 x}{2} = \frac{- 9 - 6}{2}$

Step 4.2.5.2

Subtract $6$ from $- 9$ .

$- \frac{5 x}{2} = \frac{- 15}{2}$

$- \frac{5 x}{2} = \frac{- 15}{2}$

Step 4.2.6

Move the negative in front of the fraction.

$- \frac{5 x}{2} = - \frac{15}{2}$

$- \frac{5 x}{2} = - \frac{15}{2}$

Step 4.3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 5 x = - 15$

Step 4.4

Divide each term in $- 5 x = - 15$ by $- 5$ and simplify.

Tap for more steps...

Step 4.4.1

Divide each term in $- 5 x = - 15$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 15}{- 5}$

Step 4.4.2

Simplify the left side.

Tap for more steps...

Step 4.4.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 4.4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 15}{- 5}$

Step 4.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 15}{- 5}$

$x = \frac{- 15}{- 5}$

$x = \frac{- 15}{- 5}$

Step 4.4.3

Simplify the right side.

Tap for more steps...

Step 4.4.3.1

Divide $- 15$ by $- 5$ .

$x = 3$

$x = 3$

$x = 3$

$x = 3$

Step 5

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$