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Solve for $s$ . $\newline$ $|s| + 2 \geq 18$ $\newline$ 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

s

.

\newline

|s| + 2 \geq 18

\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 expression: First, we need to isolate the absolute value expression on one side of the inequality. $\newline$ $|s| + 2 \geq 18$ $\newline$ Subtract $2$ from both sides to isolate $|s|$ . $\newline$ $|s| + 2 - 2 \geq 18 - 2$ $\newline$ $|s| \geq 16$
Set up two inequalities: Now that we have $\lvert s \rvert$ on its own, we can set up two separate inequalities to solve for $s$ because the absolute value of $s$ can be either positive or negative. $\newline$ The two inequalities are: $\newline$ $s \geq 16$ and $-s \geq 16$
Solve second inequality: To solve the second inequality, $-s \geq 16$ , we need to multiply both sides by $-1$ . Remember that when we multiply or divide an inequality by a negative number, we must reverse the inequality sign. $\newline$ $-s \geq 16$ $\newline$ $(-1)(-s) \leq (-1)(16)$ $\newline$ $s \leq -16$
Final compound inequality: Now we have two inequalities that represent the solution to the original problem: $\newline$ $s \geq 16$ or $s \leq -16$ $\newline$ This is the compound inequality that represents all the possible values of $s$ that satisfy the original inequality.

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

Posted 2 months ago

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}

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 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