Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $d$ . $|d| - 1 < 17$ 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

d

.

|d| - 1 < 17

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: $\newline$ $|d| - 1 < 17$ $\newline$ First, we isolate the absolute value term by adding $1$ to both sides of the inequality. $\newline$ $|d| - 1 + 1 < 17 + 1$ $\newline$ $|d| < 18$
Consider Absolute Value Definition: Now we need to consider the definition of absolute value. The inequality $|d| < 18$ means that $d$ is less than $18$ units away from $0$ on the number line. This gives us two inequalities: $\newline$ $d < 18$ and $-d < 18$
Multiply by $-1$ : The second inequality, $-d < 18$ , can be multiplied by $-1$ to get $d > -18$ . Remember that multiplying or dividing an inequality by a negative number reverses the inequality sign. $\newline$ $-d < 18$ $\newline$ $(-1)(-d) > (-1)(18)$ $\newline$ $d > -18$
Combine Inequalities: Combining the two inequalities from the previous steps, we get the compound inequality: $\newline$ $-18 < d < 18$ $\newline$ This means that $d$ is greater than $-18$ and less than $18$ .

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