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Solve for $u$ . $\newline$ $|-4u| \geq 20$ $\newline$ $\newline$ 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. $\newline$ ______ $\newline$

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Solve absolute value inequalities

Full solution

Q. Solve for

u

.

\newline

|-4u| \geq 20

\newline

\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

______

\newline

Given Inequality: We have the inequality: $\newline$ $|-4u| \geq 20$ $\newline$ First, we solve for $|-4u|$ . $\newline$ $|-4u| \geq 20$ means that the absolute value of $-4u$ is greater than or equal to $20$ .
Split into Two Inequalities: The absolute value inequality $|-4u| \geq 20$ can be split into two separate inequalities: $\newline$ $-4u \geq 20$ or $-4u \leq -20$ $\newline$ This is because the absolute value of a number is the distance from zero, so it can be either positive or negative.
Solve First Inequality: Solve the first inequality $-4u \geq 20$ . $\newline$ Divide both sides by $-4$ to isolate $u$ . Remember that dividing by a negative number reverses the inequality sign. $\newline$ $-4u / -4 \leq 20 / -4$ $\newline$ $u \leq -5$
Solve Second Inequality: Solve the second inequality $-4u \leq -20$ . $\newline$ Divide both sides by $-4$ to isolate $u$ . Again, remember that dividing by a negative number reverses the inequality sign. $\newline$ $-4u / -4 \geq -20 / -4$ $\newline$ $u \geq 5$
Combine Results: Combine the results from Step $3$ and Step $4$ to write the compound inequality. $\newline$ The compound inequality is: $\newline$ $u \leq -5$ or $u \geq 5$

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

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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

\frac{2}{3}

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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.)

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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 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