Algebra Examples

$4 x + y = 26$ $y = \frac{9}{2} x - 8$

Step 1

Subtract $4 x$ from both sides of the equation.

$y = 26 - 4 x$

$y = \frac{9}{2} x - 8$

Step 2

Replace all occurrences of $y$ with $26 - 4 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $y = 26 - 4 x$ with $26 - 4 x$ .

$26 - 4 x = 26 - 4 x$

$y = \frac{9}{2} x - 8$

Step 2.2

Simplify the left side.

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Step 2.2.1

Remove parentheses.

$26 - 4 x = 26 - 4 x$

$y = \frac{9}{2} x - 8$

$26 - 4 x = 26 - 4 x$

$y = \frac{9}{2} x - 8$

Step 2.3

Replace all occurrences of $y$ in $y = \frac{9}{2} x - 8$ with $26 - 4 x$ .

$26 - 4 x = \frac{9}{2} x - 8$

$26 - 4 x = 26 - 4 x$

Step 2.4

Simplify $26 - 4 x = \frac{9}{2} x - 8$ .

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Step 2.4.1

Simplify the left side.

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Step 2.4.1.1

Remove parentheses.

$26 - 4 x = \frac{9}{2} x - 8$

$26 - 4 x = 26 - 4 x$

$26 - 4 x = \frac{9}{2} x - 8$

$26 - 4 x = 26 - 4 x$

Step 2.4.2

Simplify the right side.

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Step 2.4.2.1

Combine $\frac{9}{2}$ and $x$ .

$26 - 4 x = \frac{9 x}{2} - 8$

$26 - 4 x = 26 - 4 x$

$26 - 4 x = \frac{9 x}{2} - 8$

$26 - 4 x = 26 - 4 x$

$26 - 4 x = \frac{9 x}{2} - 8$

$26 - 4 x = 26 - 4 x$

$26 - 4 x = \frac{9 x}{2} - 8$

$26 - 4 x = 26 - 4 x$

Step 3

Remove any equations from the system that are always true.

$26 - 4 x = \frac{9 x}{2} - 8$

Step 4

Solve for $x$ in $26 - 4 x = \frac{9 x}{2} - 8$ .

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Step 4.1

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

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Step 4.1.1

Subtract $\frac{9 x}{2}$ from both sides of the equation.

$26 - 4 x - \frac{9 x}{2} = - 8$

Step 4.1.2

To write $- 4 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$26 - 4 x \cdot \frac{2}{2} - \frac{9 x}{2} = - 8$

Step 4.1.3

Combine $- 4 x$ and $\frac{2}{2}$ .

$26 + \frac{- 4 x \cdot 2}{2} - \frac{9 x}{2} = - 8$

Step 4.1.4

Combine the numerators over the common denominator.

$26 + \frac{- 4 x \cdot 2 - 9 x}{2} = - 8$

Step 4.1.5

Simplify each term.

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Step 4.1.5.1

Simplify the numerator.

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Step 4.1.5.1.1

Factor $x$ out of $- 4 x \cdot 2 - 9 x$ .

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Step 4.1.5.1.1.1

Factor $x$ out of $- 4 x \cdot 2$ .

$26 + \frac{x (- 4 \cdot 2) - 9 x}{2} = - 8$

Step 4.1.5.1.1.2

Factor $x$ out of $- 9 x$ .

$26 + \frac{x (- 4 \cdot 2) + x \cdot - 9}{2} = - 8$

Step 4.1.5.1.1.3

Factor $x$ out of $x (- 4 \cdot 2) + x \cdot - 9$ .

$26 + \frac{x (- 4 \cdot 2 - 9)}{2} = - 8$

$26 + \frac{x (- 4 \cdot 2 - 9)}{2} = - 8$

Step 4.1.5.1.2

Multiply $- 4$ by $2$ .

$26 + \frac{x (- 8 - 9)}{2} = - 8$

Step 4.1.5.1.3

Subtract $9$ from $- 8$ .

$26 + \frac{x \cdot - 17}{2} = - 8$

$26 + \frac{x \cdot - 17}{2} = - 8$

Step 4.1.5.2

Move $- 17$ to the left of $x$ .

$26 + \frac{- 17 \cdot x}{2} = - 8$

Step 4.1.5.3

Move the negative in front of the fraction.

$26 - \frac{17 x}{2} = - 8$

$26 - \frac{17 x}{2} = - 8$

$26 - \frac{17 x}{2} = - 8$

Step 4.2

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

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Step 4.2.1

Subtract $26$ from both sides of the equation.

$- \frac{17 x}{2} = - 8 - 26$

Step 4.2.2

Subtract $26$ from $- 8$ .

$- \frac{17 x}{2} = - 34$

$- \frac{17 x}{2} = - 34$

Step 4.3

Multiply both sides of the equation by $- \frac{2}{17}$ .

$- \frac{2}{17} (- \frac{17 x}{2}) = - \frac{2}{17} \cdot - 34$

Step 4.4

Simplify both sides of the equation.

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Step 4.4.1

Simplify the left side.

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Step 4.4.1.1

Simplify $- \frac{2}{17} (- \frac{17 x}{2})$ .

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Step 4.4.1.1.1

Cancel the common factor of $2$ .

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Step 4.4.1.1.1.1

Move the leading negative in $- \frac{2}{17}$ into the numerator.

$\frac{- 2}{17} (- \frac{17 x}{2}) = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.1.2

Move the leading negative in $- \frac{17 x}{2}$ into the numerator.

$\frac{- 2}{17} \cdot \frac{- 17 x}{2} = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{17} \cdot \frac{- 17 x}{2} = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{17} \cdot \frac{- 17 x}{2} = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{17} (- 17 x) = - \frac{2}{17} \cdot - 34$

$\frac{- 1}{17} (- 17 x) = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.2

Cancel the common factor of $17$ .

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Step 4.4.1.1.2.1

Factor $17$ out of $- 17 x$ .

$\frac{- 1}{17} (17 (- x)) = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{17} (17 (- x)) = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{2}{17} \cdot - 34$

$- - x = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.3

Multiply.

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Step 4.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{2}{17} \cdot - 34$

Step 4.4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{2}{17} \cdot - 34$

$x = - \frac{2}{17} \cdot - 34$

$x = - \frac{2}{17} \cdot - 34$

$x = - \frac{2}{17} \cdot - 34$

Step 4.4.2

Simplify the right side.

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Step 4.4.2.1

Simplify $- \frac{2}{17} \cdot - 34$ .

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Step 4.4.2.1.1

Cancel the common factor of $17$ .

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Step 4.4.2.1.1.1

Move the leading negative in $- \frac{2}{17}$ into the numerator.

$x = \frac{- 2}{17} \cdot - 34$

Step 4.4.2.1.1.2

Factor $17$ out of $- 34$ .

$x = \frac{- 2}{17} \cdot (17 (- 2))$

Step 4.4.2.1.1.3

Cancel the common factor.

$x = \frac{- 2}{17} \cdot (17 \cdot - 2)$

Step 4.4.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 2$

$x = - 2 \cdot - 2$

Step 4.4.2.1.2

Multiply $- 2$ by $- 2$ .

$x = 4$

$x = 4$

$x = 4$

$x = 4$

$x = 4$

Step 5

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