Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $w$ . $\newline$ $|2w| < 10$ $\newline$ 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

w

.

\newline

|2w| < 10

\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 absolute value: We are given the inequality $|2w| < 10$ and we need to solve for $w$ . First, we will isolate the absolute value expression on one side of the inequality. $|2w| < 10$
Consider definition of absolute value: Next, we will consider the definition of absolute value. The absolute value of a number is less than $10$ if the number itself is between $-10$ and $10$ . So, we can write the inequality without the absolute value as: $-10 < 2w < 10$
Solve for $w$ by dividing: Now, we will solve for $w$ by dividing the entire inequality by $2$ , which is the coefficient of $w$ . $\newline$ $-10 / 2 < 2w / 2 < 10 / 2$ $\newline$ $-5 < w < 5$

More problems from Solve absolute value inequalities

Question

r

\newline

7|r| \geq 7

\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 1 month ago

Question

v

|{-4v}| \leq 4

Write a compound inequality like

1 < x < 3

x < 1

x > 3

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

Posted 1 month ago

Question

z

\newline

|-2z| \leq 18

\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 1 month ago

Question

w

\newline

|w + 8| < 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 1 month ago

Question

d

|d| + 5 > 15

Write a compound inequality like

1 < x < 3

x < 1

x > 3

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

Posted 1 month ago

Question

w

\newline

|-w| \leq 12

\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 1 month ago

Question

r

|r - 8| \geq 8

Write a compound inequality like

1 < x < 3

x < 1

x > 3

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

Posted 1 month ago

Question

t

\newline

|-9t| < 18

\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 1 month ago

Question

r

\newline

|9r| = 0

\newline

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

\newline

r =

r =

Posted 1 month ago

Question

Answer the questions below about the quadratic function.

\newline

f(x)=-3 x^{2}+6 x-5

\newline

Does the function have a minimum or maximum value?

\newline

\newline

\newline

What is the function's minimum or maximum value?

\newline

\square

\newline

Where does the minimum or maximum value occur?

\newline

x=

\newline

\square

Posted 4 hours ago