Find the x and y Intercepts f(x)=|3x+1|-8

$f (x) = | 3 x + 1 | - 8$

Find the x-intercepts.

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

$0 = | 3 x + 1 | - 8$

Solve the equation.

Rewrite the equation as $| 3 x + 1 | - 8 = 0$ .

$| 3 x + 1 | - 8 = 0$

Add $8$ to both sides of the equation.

$| 3 x + 1 | = 8$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$3 x + 1 = \pm 8$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$3 x + 1 = 8$

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

Subtract $1$ from both sides of the equation.

$3 x = 8 - 1$

Subtract $1$ from $8$ .

$3 x = 7$

Divide each term in $3 x = 7$ by $3$ and simplify.

Divide each term in $3 x = 7$ by $3$ .

$\frac{3 x}{3} = \frac{7}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{7}{3}$

Divide $x$ by $1$ .

$x = \frac{7}{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$3 x + 1 = - 8$

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

Subtract $1$ from both sides of the equation.

$3 x = - 8 - 1$

Subtract $1$ from $- 8$ .

$3 x = - 9$

Divide each term in $3 x = - 9$ by $3$ and simplify.

Divide each term in $3 x = - 9$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{7}{3}, - 3$

x-intercept(s) in point form.

x-intercept(s): $(\frac{7}{3}, 0), (- 3, 0)$

Find the y-intercepts.

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

$y = | 3 (0) + 1 | - 8$

Simplify $| 3 (0) + 1 | - 8$ .

Simplify each term.

Multiply $3$ by $0$ .

$y = | 0 + 1 | - 8$

Add $0$ and $1$ .

$y = | 1 | - 8$

The absolute value is the distance between a number and zero. The distance between $0$ and $1$ is $1$ .

$y = 1 - 8$

Subtract $8$ from $1$ .

$y = - 7$

y-intercept(s) in point form.

y-intercept(s): $(0, - 7)$

List the intersections.

x-intercept(s): $(\frac{7}{3}, 0), (- 3, 0)$

y-intercept(s): $(0, - 7)$

Find the x and y Intercepts f(x)=|3x+1|-8

Related Questions

Support LCMGCF.com by disabling your adblocker.