Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $f$ . $\newline$ $|f + 3| = 2$ $\newline$ Write your answers as integers or as proper or improper fractions in simplest form. $\newline$ $f =$ _ or $f =$ _

View step-by-step help

View step-by-step help

Solve absolute value equations

Full solution

Q. Solve for

f

.

\newline

|f + 3| = 2

\newline

Write your answers as integers or as proper or improper fractions in simplest form.

\newline

f =

_____ or

f =

_____

Understand absolute value equation: Understand the absolute value equation. $\newline$ The equation $|f + 3| = 2$ means that the expression inside the absolute value, $f + 3$ , can either be $2$ or $-2$ , because the absolute value of a number is its distance from zero on the number line, which is always non-negative.
Set up two equations: Set up two separate equations to solve for $f$ . Since $|f + 3|$ can be either $2$ or $-2$ , we have two cases: Case $1$ : $f + 3 = 2$ Case $2$ : $f + 3 = -2$
Solve first case: Solve the first case. $\newline$ For the first case, subtract $3$ from both sides to isolate $f$ : $\newline$ $f + 3 = 2$ $\newline$ $f = 2 - 3$ $\newline$ $f = -1$
Solve second case: Solve the second case. $\newline$ For the second case, subtract $3$ from both sides to isolate $f$ : $\newline$ $f + 3 = -2$ $\newline$ $f = -2 - 3$ $\newline$ $f = -5$

More problems from Solve absolute value equations

Question

3 n^{2}=27

\newline

What are the solutions to the given equation?

\newline

1

\newline

n=\sqrt{3}

\newline

n=3

\newline

n=-\sqrt{3}

n=\sqrt{3}

\newline

n=-3

n=3

Posted 10 months ago

Question

6=3 x

, what is the value of

x

Posted 2 months ago

Question

9=9 x

, what is the value of

x

Posted 2 months ago

Question

\frac{1}{2} c^{2}+3 c=1

\newline

c=f

c=g

be the solutions to the given equation. If

f>g

, which of the following is the value of

f

\newline

1

\newline

-3+\sqrt{2}

\newline

-3+\sqrt{11}

\newline

3+\sqrt{2}

\newline

3+\sqrt{11}

Posted 8 months ago

Question

Find the value of

x

that solves the equation

\ln (x-3)=1+\ln 2

\newline

Posted 9 months ago

Question

Find the value of

x

that solves the equation

\ln (x-1)+\ln 5=2

\newline

Posted 9 months ago

Question

Find the value of

x

that solves the equation

\ln (x+3)-\ln 2=0

\newline

Posted 9 months ago

Question

Find the value of

x

that solves the equation

\ln (x-3)-3 \ln 4=\ln 10

\newline

x=

Posted 9 months ago

Question

Find the value of `x`

\newline

6x+32=8x-8

Posted 8 months ago

Question

\$200

with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get

40

hats. If Aiden purchases only t-shirts, he will get

80

t-shirts. Which of the following best models the relationship between the number of hats,

h

, and the number of t-shirts,

t

, that Aiden could purchase with this money?

\newline

1

\newline

40h+80t=400

\newline

80h+40t=200

\newline

5h+2.5t=200

\newline

2.5h+5t=200

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant