Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $y$ . $\newline$ |y| + 9 < 13 $\newline$ Write a compound inequality like 1 < x < 3 or like x < 1 or x > 3. Use integers, proper fractions, or improper fractions in simplest form. $\newline$ ______

View step-by-step help

View step-by-step help

Solve absolute value inequalities

Full solution

Q. Solve for

y

.

\newline

|y| + 9 < 13

\newline

Write a compound inequality like

1 < x < 3

or like

x < 1

or

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

______

Isolate $|y|$ : We have the inequality: $\newline$ |y| + 9 < 13 $\newline$ First, we isolate $|y|$ by subtracting $9$ from both sides of the inequality. $\newline$ |y| + 9 - 9 < 13 - 9 $\newline$ |y| < 4
Interpret absolute value inequality: Now we interpret the absolute value inequality. The expression |y| < 4 means that $y$ is less than $4$ units away from $0$ on the number line. This gives us two inequalities: $\newline$ y < 4 and y > -4
Combine into compound inequality: We can combine these two inequalities into a compound inequality: $\newline$ -4 < y < 4 $\newline$ This compound inequality represents all the values of $y$ that are more than $-4$ and less than $4$ .

More problems from Solve absolute value inequalities

Question

u

\newline

|u| - 4 \geq 6

\newline

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

Posted 5 months ago

Question

9 \frac{7}{8}

into an improper fraction.

\newline

Posted 8 months ago

Question

f(x)=\left\{\begin{array}{lll} -4 x & \text { for } & x<-1 \\ -x+1 & \text { for } & -1 \leq x \leq 3 \\ -2 x+8 & \text { for } & x>3 \end{array}\right.

\newline

f(3)

\newline

\newline

Posted 8 months ago

Question

Solve the system of equations.

\newline

\begin{array}{l}y=22 x-38 \\y=x^{2}+11 x-14\end{array}

\newline

Write the coordinates in exact form. Simplify all fractions and radicals.

\newline

\begin{array}{l}(-,-) \\(-,-)\end{array}

Posted 6 months ago

Question

A baseball player went up to bat

250

times in a season. He hit the ball

100

times. Find the rate of balls hit to times at bat. Express as a simplified fraction.

\newline

\frac{2}{5}

\newline

\frac{5}{2}

\newline

\frac{3}{5}

\newline

\frac{2}{3}

Posted 9 months ago

Question

Eric is sorting pencils into boxes. He put

16

pencils in the first box,

21

pencils in the second box,

26

pencils in the third box, and

31

pencils in the fourth box. What kind of sequence is this?

\newline

\newline

\newline

\newline

\newline

Posted 8 months ago

Question

Given the definitions of

f(x)

g(x)

below, find the value of

g(f(2))

\newline

\begin{array}{l} f(x)=-5 x+3 \\ g(x)=2 x^{2}+5 x-14 \end{array}

\newline

Posted 8 months ago

Question

t

\newline

|t + 8| \leq 4

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

Posted 8 months ago

Question

p

\newline

|p + 1| < 9

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

Posted 8 months ago

Question

v

\newline

-5|v| > -10

\newline

Write a compound inequality like

1 < x < 3

x < 1

x > 3

. Use integers, proper fractions, or improper fractions in simplest form.

\newline

Posted 8 months ago

Related topics

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