Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve for $t$ . $\newline$ $|t + 8| \leq 4$ $\newline$ 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. $\newline$ ______

View step-by-step help

View step-by-step help

Solve absolute value inequalities

Full solution

Q. Solve for

t

.

\newline

|t + 8| \leq 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

______

Absolute Value Inequality: We have the inequality $|t + 8| \leq 4$ . The absolute value inequality means that the expression inside the absolute value, $t + 8$ , can be either less than or equal to $4$ or greater than or equal to $-4$ . We will split this into two separate inequalities to solve for $t$ .
Case $1$ : Non-Negative Expression: First, let's consider the case where the expression inside the absolute value is non-negative: $t + 8 \leq 4$ . To find the value of $t$ , we subtract $8$ from both sides of the inequality. $\newline$ $t + 8 - 8 \leq 4 - 8$ $\newline$ $t \leq -4$
Case $2$ : Non-Positive Expression: Now, let's consider the case where the expression inside the absolute value is non-positive: $- (t + 8) \leq 4$ . This is equivalent to $-t - 8 \leq 4$ . To find the value of $t$ , we first add $8$ to both sides of the inequality. $-t - 8 + 8 \leq 4 + 8$ $-t \leq 12$ Multiplying both sides by $-1$ (and remembering to reverse the inequality sign because we are multiplying by a negative number), we get: $t \geq -12$
Combining Inequalities: Combining the two inequalities we have found, we get the compound inequality: $\newline$ $-12 \leq t \leq -4$ $\newline$ This means that $t$ must be greater than or equal to $-12$ and less than or equal to $-4$ .

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 3 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

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}

Posted 2 days 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 2 months 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

\int_{0}^{\ln 2} 3 x e^{x}\left(e^{x}-1\right)^{2} d x

Posted 11 hours ago