Questions: Solve the inequality. 2(x+4)-8>-4(x-3)+24 The solution set is (Type your answer in interval notation)

Solve the inequality. 2(x+4)-8>-4(x-3)+24 The solution set is (Type your answer in interval notation)
Transcript text: Solve the inequality. \[ 2(x+4)-8>-4(x-3)+24 \] The solution set is $\square$ (Type your answer in interval notation )
failed

Solution

failed
failed

Solution Steps

To solve the inequality \(2(x+4)-8 > -4(x-3)+24\), we will first expand and simplify both sides of the inequality. Then, we will collect all terms involving \(x\) on one side and constant terms on the other side. Finally, we will solve for \(x\) and express the solution in interval notation.

Step 1: Distribute and Simplify Both Sides

First, distribute the constants in the expressions on both sides of the inequality:

\[ 2(x+4) - 8 > -4(x-3) + 24 \]

Distribute the 2 on the left side:

\[ 2x + 8 - 8 > -4(x-3) + 24 \]

Simplify the left side:

\[ 2x > -4(x-3) + 24 \]

Distribute the -4 on the right side:

\[ 2x > -4x + 12 + 24 \]

Simplify the right side:

\[ 2x > -4x + 36 \]

Step 2: Combine Like Terms

Add \(4x\) to both sides to get all the \(x\) terms on one side:

\[ 2x + 4x > 36 \]

Combine the \(x\) terms:

\[ 6x > 36 \]

Step 3: Solve for \(x\)

Divide both sides by 6 to solve for \(x\):

\[ x > \frac{36}{6} \]

Simplify the division:

\[ x > 6 \]

Final Answer

The solution set in interval notation is:

\[ \boxed{(6, \infty)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
QUESTION 7 The smallest independently functioning biological unit of an organism is a(n) cell molecule organ tissue
failedAnswered
Given the table of probabilities for the random variable x, does this form a probability distribution? X 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42 Yes No
failedAnswered
Process p1 arrives at time 0 and will need 100 units of CPU time. Process p2 arrives at time 1 and will need 1 unit of CPU time. 1) The ATT under FIFO will be time units. 2) The ATT under SJF will be time units. 3) The ATT under SRT will be time units.
failedAnswered
Identificar la integral que representa la longitud de arco entre los puntos (1,1) y (2,16) de la curva y=x^4 A) S=integral from 1 to 2 of sqrt(1+4x^3) dx B) S=integral from 1 to 16 of sqrt(1+16x^6) dx C) S=integral from 1 to 16 of sqrt(1+4x^3) dx D) S=integral from 1 to 2 of sqrt(1+16x^6) dx
failedAnswered
The graph below shows the relationship between the value of a building and the depreciation allowed for income tax purposes. Find the slope of the line between the two points shown on the graph.