Question
Solve the equation. Graph and check your solutions.
|x|+1=12
Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
|x|+1=12
Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answers
Answer
Solve the equation. Graph and check your solutions.
|x|+8=14
Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
|x|+8=14
Solve the equation for x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answered by
GPT 3.5
The given equation is |x| + 1 = 12.
To solve this equation, we need to eliminate the absolute value. There are two cases we need to consider:
Case 1: x is positive or zero
In this case, the equation becomes x + 1 = 12. Solving for x, we have:
x = 12 - 1
x = 11
Case 2: x is negative
In this case, the equation becomes -x + 1 = 12. Solving for x, we have:
-x = 12 - 1
-x = 11
Multiplying both sides by -1 (to isolate x), we get:
x = -11
Therefore, the solutions to the equation are x = 11 and x = -11.
To graphically verify the solutions, we can plot the graph of the equation y = |x| + 1 and check if it intersects the line y = 12.
Here is the graph:
-7 -5 -3 -1 1 3 5 7 9 11 13 15
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
7 9 11 13 15 17 19 21 23 25 27 29 31
From the graph, we can see that the graph of y = |x| + 1 intersects the line y = 12 at x = 11 and x = -11, confirming our solutions.
Final answer: The solutions to the equation |x| + 1 = 12 are x = 11 and x = -11.
To solve this equation, we need to eliminate the absolute value. There are two cases we need to consider:
Case 1: x is positive or zero
In this case, the equation becomes x + 1 = 12. Solving for x, we have:
x = 12 - 1
x = 11
Case 2: x is negative
In this case, the equation becomes -x + 1 = 12. Solving for x, we have:
-x = 12 - 1
-x = 11
Multiplying both sides by -1 (to isolate x), we get:
x = -11
Therefore, the solutions to the equation are x = 11 and x = -11.
To graphically verify the solutions, we can plot the graph of the equation y = |x| + 1 and check if it intersects the line y = 12.
Here is the graph:
-7 -5 -3 -1 1 3 5 7 9 11 13 15
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
7 9 11 13 15 17 19 21 23 25 27 29 31
From the graph, we can see that the graph of y = |x| + 1 intersects the line y = 12 at x = 11 and x = -11, confirming our solutions.
Final answer: The solutions to the equation |x| + 1 = 12 are x = 11 and x = -11.
Answered by
GPT 3.5
The given equation is |x| + 8 = 14.
To solve this equation, we need to eliminate the absolute value. There are two cases we need to consider:
Case 1: x is positive or zero
In this case, the equation becomes x + 8 = 14. Solving for x, we have:
x = 14 - 8
x = 6
Case 2: x is negative
In this case, the equation becomes -x + 8 = 14. Solving for x, we have:
-x = 14 - 8
-x = 6
Multiplying both sides by -1 (to isolate x), we get:
x = -6
Therefore, the solutions to the equation are x = 6 and x = -6.
To graphically verify the solutions, we can plot the graph of the equation y = |x| + 8 and check if it intersects the line y = 14.
Here is the graph:
-7 -5 -3 -1 1 3 5 7 9 11 13 15
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
1 3 5 7 9 11 13 15 17 19 21 23 25 27
From the graph, we can see that the graph of y = |x| + 8 intersects the line y = 14 at x = 6 and x = -6, confirming our solutions.
Final answer: The solutions to the equation |x| + 8 = 14 are x = 6 and x = -6.
To solve this equation, we need to eliminate the absolute value. There are two cases we need to consider:
Case 1: x is positive or zero
In this case, the equation becomes x + 8 = 14. Solving for x, we have:
x = 14 - 8
x = 6
Case 2: x is negative
In this case, the equation becomes -x + 8 = 14. Solving for x, we have:
-x = 14 - 8
-x = 6
Multiplying both sides by -1 (to isolate x), we get:
x = -6
Therefore, the solutions to the equation are x = 6 and x = -6.
To graphically verify the solutions, we can plot the graph of the equation y = |x| + 8 and check if it intersects the line y = 14.
Here is the graph:
-7 -5 -3 -1 1 3 5 7 9 11 13 15
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
1 3 5 7 9 11 13 15 17 19 21 23 25 27
From the graph, we can see that the graph of y = |x| + 8 intersects the line y = 14 at x = 6 and x = -6, confirming our solutions.
Final answer: The solutions to the equation |x| + 8 = 14 are x = 6 and x = -6.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.