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Solve for $w$ . $\newline$ $|w| - 9 \geq -4$ $\newline$ 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. $\newline$ ______

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Solve absolute value inequalities

Full solution

Q. Solve for

w

.

\newline

|w| - 9 \geq -4

\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 term: We have the inequality: $\newline$ $|w| - 9 \geq -4$ $\newline$ First, we need to isolate the absolute value term $|w|$ on one side of the inequality.
Add $9$ to isolate: Add $9$ to both sides of the inequality to isolate $|w|$ : $|w| - 9 + 9 \geq -4 + 9$ $|w| \geq 5$
Absolute value inequality: Now we have the absolute value inequality $|w| \geq 5$ . This means that $w$ is either greater than or equal to $5$ or less than or equal to $-5$ .
Split into two inequalities: We can split the absolute value inequality into two separate inequalities: $\newline$ $w \geq 5$ or $w \leq -5$ $\newline$ This is the compound inequality that represents the solution to the original problem.

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 2 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

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Question

\newline

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}

\newline

\rightarrow

Posted 2 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

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Question

1,2,3,4,5

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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}

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Question

Eric is sorting pencils into boxes. He put

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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 1 month 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 1 month ago