Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $z$ . $|z| - 8 \leq 9$ 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.

View step-by-step help

View step-by-step help

Solve absolute value inequalities

Full solution

Q. Solve for

z

.

|z| - 8 \leq 9

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.

Isolate absolute value: We have the inequality $|z| - 8 \leq 9$ . To solve for $|z|$ , we need to isolate it on one side of the inequality. $\newline$ $|z| - 8 \leq 9$ $\newline$ $|z| - 8 + 8 \leq 9 + 8$ $\newline$ $|z| \leq 17$
Consider absolute value definition: Now that we have $|z| \leq 17$ , we need to consider the definition of absolute value. The absolute value of $z$ is less than or equal to $17$ , which means $z$ is within the range of $-17$ to $17$ . This can be written as a compound inequality: $-17 \leq z \leq 17$

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 3 months ago

Question

9 \frac{7}{8}

into an improper fraction.

\newline

Posted 2 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 2 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 3 days 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 2 months ago

Question

1,2,3,4,5

6

are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than

600

\newline

The probability that the three-digit number is even and greater than

600

\square

\newline

(Type an integer or a simplified fraction.)

Posted 2 months ago

Question

Use benchmark fractions to estimate sums and differences less than or gremet than

1

. Write each expresston in the correct answer space.

\newline

\begin{array}{l} \frac{7}{8}+\frac{5}{10} \\ 1 \frac{5}{8}-\frac{5}{6} \\ \frac{10}{10}-\frac{2}{3} \\ \frac{1}{2}+\frac{2}{3} \\ \frac{5}{12}+\frac{1}{4} \\ 1 \frac{1}{6}+\frac{7}{8} \\ \end{array}

Posted 2 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 2 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 2 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 2 months ago