Algebra Examples

f (x) = \frac{3 x}{4} + 3

$f (x) = \frac{3 x}{4} + 3$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = \frac{3 x}{4} + 3

$0 = \frac{3 x}{4} + 3$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

\frac{3 x}{4} + 3 = 0

$\frac{3 x}{4} + 3 = 0$ .

\frac{3 x}{4} + 3 = 0

$\frac{3 x}{4} + 3 = 0$

Step 1.2.2

Subtract

3

$3$ from both sides of the equation.

\frac{3 x}{4} = - 3

$\frac{3 x}{4} = - 3$

Step 1.2.3

Multiply both sides of the equation by

\frac{4}{3}

$\frac{4}{3}$ .

\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3$

Step 1.2.4

Simplify both sides of the equation.

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Step 1.2.4.1

Simplify the left side.

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Step 1.2.4.1.1

Simplify

\frac{4}{3} \cdot \frac{3 x}{4}

$\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Step 1.2.4.1.1.1

Cancel the common factor of

4

$4$ .

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Step 1.2.4.1.1.1.1

Cancel the common factor.

\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot - 3$

Step 1.2.4.1.1.1.2

Rewrite the expression.

\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3$

\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3$

Step 1.2.4.1.1.2

Cancel the common factor of

3

$3$ .

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Step 1.2.4.1.1.2.1

Factor

3

$3$ out of

3 x

$3 x$ .

\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot - 3

$\frac{1}{3} (3 (x)) = \frac{4}{3} \cdot - 3$

Step 1.2.4.1.1.2.2

Cancel the common factor.

\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3

$\frac{1}{3} (3 x) = \frac{4}{3} \cdot - 3$

Step 1.2.4.1.1.2.3

Rewrite the expression.

x = \frac{4}{3} \cdot - 3

$x = \frac{4}{3} \cdot - 3$

x = \frac{4}{3} \cdot - 3

$x = \frac{4}{3} \cdot - 3$

x = \frac{4}{3} \cdot - 3

$x = \frac{4}{3} \cdot - 3$

x = \frac{4}{3} \cdot - 3

$x = \frac{4}{3} \cdot - 3$

Step 1.2.4.2

Simplify the right side.

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Step 1.2.4.2.1

Simplify

\frac{4}{3} \cdot - 3

$\frac{4}{3} \cdot - 3$ .

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Step 1.2.4.2.1.1

Cancel the common factor of

3

$3$ .

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Step 1.2.4.2.1.1.1

Factor

3

$3$ out of

- 3

$- 3$ .

x = \frac{4}{3} \cdot (3 (- 1))

$x = \frac{4}{3} \cdot (3 (- 1))$

Step 1.2.4.2.1.1.2

Cancel the common factor.

x = \frac{4}{3} \cdot (3 \cdot - 1)

$x = \frac{4}{3} \cdot (3 \cdot - 1)$

Step 1.2.4.2.1.1.3

Rewrite the expression.

x = 4 \cdot - 1

$x = 4 \cdot - 1$

x = 4 \cdot - 1

$x = 4 \cdot - 1$

Step 1.2.4.2.1.2

Multiply

4

$4$ by

- 1

$- 1$ .

x = - 4

$x = - 4$

x = - 4

$x = - 4$

x = - 4

$x = - 4$

x = - 4

$x = - 4$

x = - 4

$x = - 4$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

(- 4, 0)

$(- 4, 0)$

x-intercept(s):

(- 4, 0)

$(- 4, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = \frac{3 (0)}{4} + 3

$y = \frac{3 (0)}{4} + 3$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

y = \frac{3 (0)}{4} + 3

$y = \frac{3 (0)}{4} + 3$

Step 2.2.2

Simplify

\frac{3 (0)}{4} + 3

$\frac{3 (0)}{4} + 3$ .

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Step 2.2.2.1

Multiply

3

$3$ by

0

$0$ .

y = \frac{0}{4} + 3

$y = \frac{0}{4} + 3$

Step 2.2.2.2

Divide

0

$0$ by

4

$4$ .

y = 0 + 3

$y = 0 + 3$

Step 2.2.2.3

Add

0

$0$ and

3

$3$ .

y = 3

$y = 3$

y = 3

$y = 3$

y = 3

$y = 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 3)

$(0, 3)$

y-intercept(s):

(0, 3)

$(0, 3)$

Step 3

List the intersections.

x-intercept(s):

(- 4, 0)

$(- 4, 0)$

y-intercept(s):

(0, 3)

$(0, 3)$

Step 4

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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