Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Graph the solution set. $\newline$ $3(4x-8)+12 > 11x-14$ $\newline$ Express the solution in set-builder notation. Select the correct choice below to complete your choice. $\newline$ A. The solution set is $\newline$ $\{x\mid x \geq \}$ . $\newline$ Use integers or fractions for any numbers in the expression $\newline$ B. The solution is all real numbers. $\newline$ C. The solution is the empty set

View step-by-step help

View step-by-step help

Solve higher-degree inequalities

Full solution

Q. Graph the solution set.

\newline

3(4x-8)+12 > 11x-14

\newline

Express the solution in set-builder notation. Select the correct choice below to complete your choice.

\newline

A. The solution set is

\newline

\{x\mid x \geq \}

.

\newline

Use integers or fractions for any numbers in the expression

\newline

B. The solution is all real numbers.

\newline

C. The solution is the empty set

Distribute and Simplify: First, we need to simplify and solve the inequality $3(4x-8)+12 > 11x-14$ . Distribute the $3$ into the parentheses: $3\times 4x - 3\times 8 + 12 > 11x - 14$ . This simplifies to $12x - 24 + 12 > 11x - 14$ .
Combine Like Terms: Next, combine like terms on the left side of the inequality: $12x - 12 > 11x - 14$ .
Isolate $x$ : Now, subtract $11x$ from both sides to get $x$ on one side of the inequality: $12x - 11x - 12 > -14$ . This simplifies to $x - 12 > -14$ .
Add and Subtract: Then, add $12$ to both sides of the inequality to isolate $x$ : $x - 12 + 12 > -14 + 12$ . This simplifies to $x > -2$ .
Final Solution: The solution to the inequality is all $x$ values greater than $-2$ . In set-builder notation, this is expressed as $\{x | x > -2\}$ .

More problems from Solve higher-degree inequalities

Question

Find the solution of the linear inequality. Express the solution set in set-builder notation. Select the correct choice below to complete your choice.

\newline

A. The solution set is

\{x \mid \}

\newline

(Use integers or fractions for any numbers in the expression)

\newline

B. The solution is all real numbers.

\newline

C. The solution set is the empty set.

Posted 3 months ago

Question

f

g

are defined as follows.

\newline

\begin{align*} &f(x) = \frac{x-2}{x^2 + 4x - 12},\ &g(x) = \frac{x}{x^2 + 64} \end{align*}

\newline

For each function, find the domain.

\newline

Write each answer as an interval or union of intervals.

Posted 3 months ago

Question

C=0.25(L-1200)

\newline

C

, in dollars, to the holder of a liability insurance account given a total liability of

L

dollars is given by the equation as long as

C

is positive. By how many dollars does the liability increase when the cost to the holder increases by

1

\newline

\square

Posted 18 hours ago

Question

Which of the following is an equation of the line in the

x y

x

-\frac{2}{7}

y

\frac{8}{7}

\newline

1

\newline

7 y-28 x=8

\newline

7 y+28 x=8

\newline

-7 y+28 x=8

\newline

-7 y-28 x=8

Posted 18 hours ago

Question

In which of the following does the shaded region represent the solution set to

y \leq \frac{3}{2} x+2

\newline

1

\newline

\newline

\newline

\newline

Posted 18 hours ago

Question

\newline

4

\newline

\newline

\newline

\newline

\newline

\newline

\newline

\newline

0.23-A

\newline

\newline

1

\newline

05

28

2024

\newline

2

23

24

7

6.23 /

\newline

2

. Wholesome Pizza surveyed a random sample of

40

Trinity Food Festival attendees about their favorite tpe of plza. of the aneor . Food Festival attendees.

\newline

Based on the data, what is the most reasonable estimate for the number of Trinity Food Festival attendees whose fororth

Posted 18 hours ago

Question

Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a

d

delivery fee and

p

per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under

T

. Each pizza is cut into

s

slices, and she wonders how many total slices she can afford. Let

n

represent the number of pizzas that Jacque buys.

\newline

1

) Which inequality describes this scenario? Choose

1

\newline

(Choice A, Checked)

A

\newline

B

\newline

C

\newline

D

\newline

2

) What is the largest number of slices that Jacque can afford?

Posted 18 hours ago

Question

What is the radius of the circle

(x-9)^{2}+(y+4)^{2}=\frac{529}{4} ?

\newline

Write your answer in simplified, rationalized form.

Posted 18 hours ago

Question

What is the radius of the circle

\left(x-\frac{14}{3}\right)^{2}+y^{2}=121 ?

\newline

Write your answer in simplified, rationalized form.

Posted 18 hours ago

Question

What is the radius of the circle

x^{2}+(y+5)^{2}=9 ?

\newline

Write your answer in simplified, rationalized form.

Posted 18 hours ago