Question

Question 5 of 6What is the graph of the solution to the following compound inequality?7x+3 2 52or3-x>9O A.-10-9-8-7-6-5 -4 -3 -2 -101 2345 6789 10B.-10 -9 -8 -7 -6 -5 -4 -3 -2 -1012 3 45678910C.-10 -9 -8 -7 -6 -5 -4-3-2 -10123456789 10O D.-10 -9 -8 -7 -6 -5 -4 -3-2 -10123 456789 10SUBMIT

Answer 1

The compound inequality 7x + 3 ≥ 52 or 3 - x > 9 has solutions x ≥ 7 and x < -6. The graph should use a filled circle at 7 and an open circle at -6 indicating that the values are greater than or equal to 7 and less than -6, respectively. Option C is the correct graphical representation.

Step-by-step explanation:

To solve the compound inequality 7x + 3 ≥ 52 or 3 - x > 9, we need to solve each part of the inequality separately and then combine the solutions.

First, let's solve 7x + 3 ≥ 52:

Subtract 3 from both sides: 7x ≥ 49

Divide both sides by 7: x ≥ 7

Second, we solve 3 - x > 9:

Subtract 3 from both sides: -x > 6

Multiply both sides by -1 and remember to reverse the inequality: x < -6

Combining the solutions, we have x ≥ 7 or x < -6. This means that the solution to the compound inequality includes all real numbers less than -6 or greater than or equal to 7. When graphing this inequality, a filled circle should be used at 7 to indicate that 7 is included in the solution. At -6, an open circle should be used to show that -6 is not included. The answer that correctly represents this solution graphically is option C.

Answer 2

7x + 3 ≥ 52

or

3 - x > 9

`\begin{gathered} 7x+3\ge52 \\ -3 \\ 52-3=49 \\ 7x=49 \\ /7 \\ 49/7=7 \\ x\ge7 \end{gathered}`
`\begin{gathered} 3-x>9 \\ -3 \\ 9-3\text{ = 6} \\ x\text{ >-6} \end{gathered}`

Given the information

x is greater then -6 so the circle will not be filled

while x is greater than or equal to 7 so the circle will be filled

The answer is the option C.