Which of the following values are solutions to the inequality 5, is less than, 7, plus, 5, x, question mark5<7+5x?
I., 6, II., minus, 5, III., minus, 7
I.6II.−5III.−7
Answer
Attempt 1 out of 3
Multiple Choice Answers
NoneNone
I onlyI only
II onlyII only
III onlyIII only
I and III and II
I and IIII and III
II and IIIII and III
I, II and IIII, II and III
To find the solutions to the inequality, start by simplifying the right side of the inequality: 7 + 5x = 12 + 5x.
Now, the inequality becomes: 5 < 12 + 5x.
To find the interval where the inequality holds true, subtract 12 from both sides: -7 < 5x.
Now divide both sides by 5: -7/5 < x.
So, the solutions to the inequality are all values of x greater than -7/5.
Therefore, the correct answer is II only (x = -5).
Incorrect you have two more chances
Apologies for the incorrect response. Let's solve the inequality again:
We have the inequality 5 < 7 + 5x.
Let's simplify the right side of the inequality: 7 + 5x = 12 + 5x.
Now the inequality becomes 5 < 12 + 5x.
To find the interval where the inequality holds true, subtract 12 from both sides: -7 < 5x.
Dividing both sides by 5, we get: -7/5 < x.
Therefore, x is greater than -7/5. This means that x can take any value greater than -7/5.
So, the correct answer is I, II, and III (6, -5, and -7).
Incorrect you have one more try
Apologies for the mistake. Let's solve the inequality again:
We have the inequality 5 < 7 + 5x.
Let's simplify the right side of the inequality: 7 + 5x.
Now the inequality becomes 5 < 12 + 5x.
Subtracting 12 from both sides, we get: -7 < 5x.
Dividing both sides by 5 (remember to reverse the inequality when dividing by a negative number), we obtain: -7/5 > x.
So, the value of x must be less than -7/5.
Therefore, the correct answer is III only (-7).
I apologize for any confusion caused.
To find the values that are solutions to the inequality 5 < 7 + 5x, we can solve this inequality algebraically.
First, subtract 7 from both sides to isolate the term 5x:
5 - 7 < 7 + 5x - 7
Resulting in:
-2 < 5x
Next, divide both sides by 5 to solve for x:
-2/5 < 5x/5
which simplifies to:
-2/5 < x
or
x > -2/5
Now, we can analyze the answer choices:
I. 6: Since 6 is greater than -2/5, it satisfies the inequality.
II. -5: -5 is less than -2/5, so it does not satisfy the inequality.
III. -7: -7 is less than -2/5, so it also does not satisfy the inequality.
Therefore, the only value that is a solution to the inequality is I. 6