Algebra Examples

$\frac{x}{2} - \frac{y}{3} = \frac{5}{6}$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$\frac{x}{2} - \frac{0}{3} = \frac{5}{6}$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify $\frac{x}{2} - \frac{0}{3}$ .

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Step 1.2.1.1

Divide $0$ by $3$ .

$\frac{x}{2} - 0 = \frac{5}{6}$

Step 1.2.1.2

Subtract $0$ from $\frac{x}{2}$ .

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

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

Step 1.2.2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (\frac{5}{6})$

Step 1.2.3

Simplify both sides of the equation.

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Step 1.2.3.1

Simplify the left side.

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Step 1.2.3.1.1

Cancel the common factor of $2$ .

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Step 1.2.3.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (\frac{5}{6})$

Step 1.2.3.1.1.2

Rewrite the expression.

$x = 2 (\frac{5}{6})$

$x = 2 (\frac{5}{6})$

$x = 2 (\frac{5}{6})$

Step 1.2.3.2

Simplify the right side.

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Step 1.2.3.2.1

Cancel the common factor of $2$ .

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Step 1.2.3.2.1.1

Factor $2$ out of $6$ .

$x = 2 \frac{5}{2 (3)}$

Step 1.2.3.2.1.2

Cancel the common factor.

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

Step 1.2.3.2.1.3

Rewrite the expression.

$x = \frac{5}{3}$

$x = \frac{5}{3}$

$x = \frac{5}{3}$

$x = \frac{5}{3}$

$x = \frac{5}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{5}{3}, 0)$

x-intercept(s): $(\frac{5}{3}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$\frac{0}{2} - \frac{y}{3} = \frac{5}{6}$

Step 2.2

Solve the equation.

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Step 2.2.1

Combine the opposite terms in $\frac{0}{2} - \frac{y}{3}$ .

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Step 2.2.1.1

Divide $0$ by $2$ .

$0 - \frac{y}{3} = \frac{5}{6}$

Step 2.2.1.2

Subtract $\frac{y}{3}$ from $0$ .

$- \frac{y}{3} = \frac{5}{6}$

$- \frac{y}{3} = \frac{5}{6}$

Step 2.2.2

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{y}{3}) = - 3 (\frac{5}{6})$

Step 2.2.3

Simplify both sides of the equation.

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Step 2.2.3.1

Simplify the left side.

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Step 2.2.3.1.1

Simplify $- 3 (- \frac{y}{3})$ .

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Step 2.2.3.1.1.1

Cancel the common factor of $3$ .

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Step 2.2.3.1.1.1.1

Move the leading negative in $- \frac{y}{3}$ into the numerator.

$- 3 \frac{- y}{3} = - 3 (\frac{5}{6})$

Step 2.2.3.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- y}{3} = - 3 (\frac{5}{6})$

Step 2.2.3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- y}{3} = - 3 (\frac{5}{6})$

Step 2.2.3.1.1.1.4

Rewrite the expression.

$- - y = - 3 (\frac{5}{6})$

$- - y = - 3 (\frac{5}{6})$

Step 2.2.3.1.1.2

Multiply.

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Step 2.2.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 y = - 3 (\frac{5}{6})$

Step 2.2.3.1.1.2.2

Multiply $y$ by $1$ .

$y = - 3 (\frac{5}{6})$

$y = - 3 (\frac{5}{6})$

$y = - 3 (\frac{5}{6})$

$y = - 3 (\frac{5}{6})$

Step 2.2.3.2

Simplify the right side.

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Step 2.2.3.2.1

Cancel the common factor of $3$ .

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Step 2.2.3.2.1.1

Factor $3$ out of $- 3$ .

$y = 3 (- 1) \frac{5}{6}$

Step 2.2.3.2.1.2

Factor $3$ out of $6$ .

$y = 3 \cdot - 1 \frac{5}{3 \cdot 2}$

Step 2.2.3.2.1.3

Cancel the common factor.

$y = 3 \cdot - 1 \frac{5}{3 \cdot 2}$

Step 2.2.3.2.1.4

Rewrite the expression.

$y = - \frac{5}{2}$

$y = - \frac{5}{2}$

$y = - \frac{5}{2}$

$y = - \frac{5}{2}$

$y = - \frac{5}{2}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{2})$

y-intercept(s): $(0, - \frac{5}{2})$

Step 3

List the intersections.

x-intercept(s): $(\frac{5}{3}, 0)$

y-intercept(s): $(0, - \frac{5}{2})$

Step 4

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