Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the solution to the compound inequality in inteval notation?

2(x+3) > 6" or "2x+3 <= -7

What is the solution to the compound inequality in inteval notation? $\newline$ 2(x+3)>6 \text { or } 2 x+3 \leq-7

View step-by-step help

View step-by-step help

Does (x, y) satisfy the inequality?

Full solution

Q. What is the solution to the compound inequality in inteval notation?

\newline

2(x+3)>6 \text { or } 2 x+3 \leq-7

Distribute and Simplify: Solve the first inequality 2(x+3) > 6. First, distribute the $2$ to both terms inside the parentheses: 2\times x + 2\times 3 > 6, which simplifies to 2x + 6 > 6.
Subtract to Isolate Variable: Subtract $6$ from both sides of the inequality 2x + 6 > 6 to isolate the term with the variable: 2x + 6 - 6 > 6 - 6, which simplifies to 2x > 0.
Divide to Solve for x: Divide both sides of the inequality 2x > 0 by $2$ to solve for $x$ : \frac{2x}{2} > \frac{0}{2}, which simplifies to x > 0.
Subtract to Isolate Variable: Solve the second inequality $2x + 3 \leq -7$ . Subtract $3$ from both sides of the inequality to isolate the term with the variable: $2x + 3 - 3 \leq -7 - 3$ , which simplifies to $2x \leq -10$ .
Divide to Solve for $x$ : Divide both sides of the inequality $2x \leq -10$ by $2$ to solve for $x$ : $\frac{2x}{2} \leq \frac{-10}{2}$ , which simplifies to $x \leq -5$ .
Combine Solutions: Combine the solutions of the two inequalities to express the solution of the compound inequality. $\newline$ The first inequality gives us x > 0, and the second inequality gives us $x \leq -5$ . Since these are connected by ＂or,＂ we take the union of the two solutions.
Express in Interval Notation: Express the solution in interval notation. $\newline$ The solution to x > 0 is $(0, \infty)$ , and the solution to $x \leq -5$ is $(-\infty, -5]$ . Since we are looking for the union of these two solutions, the interval notation for the compound inequality is $(-\infty, -5] \cup (0, \infty)$ .

More problems from Does (x, y) satisfy the inequality?

Question

Write the following inequality in slope-intercept form.

\newline

9x+y \geq -17

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

\newline

Posted 5 months ago

Question

(2,\,1)

make the inequality

2x + 15y < 20

\newline

\newline

\newline

Posted 5 months ago

Question

Jack is fixing up his home and must spend less than

\$4,800

to hire carpenters and painters. Carpenters charge

\$60

per hour and painters charge

\$32

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours of carpentry

\newline

y =

the number of hours of painting

\newline

\newline

32x + 60y < 4,800

\newline

60x + 32y < 4,800

\newline

32x - 60y < 4,800

\newline

60x - 32y < 4,800

Posted 5 months ago

Question

(2,\, 10)

a solution to this system of inequalities?

\newline

y \geq x + 10

\newline

y \leq 9x + 5

\newline

\newline

\newline

Posted 5 months ago

Question

Write the following inequality in slope-intercept form.

\newline

4x - 2y \leq 8

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 9 months ago

Question

Write the following inequality in slope-intercept form.

\newline

-3x + 5y > 15

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 9 months ago

Question

Write the following inequality in slope-intercept form.

\newline

2x + 3y < -6

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 9 months ago

Question

Write the following inequality in slope-intercept form.

\newline

-7x - y \geq 21

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 8 months ago

Question

Write the following inequality in slope-intercept form.

\newline

5x - 4y > -20

\newline

Write your answer with

y

first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.

Posted 9 months ago

Question

Miyoko's goal is to earn more than

(950

this week. She earns

)250

for every day she works as a cryptographer, and earns

\$180

for every day she works as a geologist.

\newline

Write an inequality that represents the number of days Miyoko should work as a cryptographer

C

and as a geologist

G

to achieve her goal.

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant