Statement 1: 6 – 5x > -13
This statement provides an additional inequality. By solving this inequality, we can determine the range of values for x. Solving it:
6 - 5x > -13
Add 5x to both sides:
6 > -13 + 5x
19 > 5x
Divide both sides by 5 (since the inequality sign doesn't change when dividing by a positive number):
19/5 > x
x < 19/5
Statement 1 alone is sufficient to determine a range for x, but it doesn't provide an exact value for x.
Statement 2: 3 – 2x < -x + 4 < 7.2 – 2x
This statement provides a compound inequality. By solving this compound inequality, we can determine the range of values for x. Solving it:
3 - 2x < -x + 4 < 7.2 - 2x
We can simplify it by subtracting x from all parts of the inequality:
3 - 3x < 4 < 7.2 - 3x
Simplify further:
-3x + 3 < 4 < -3x + 7.2
Now we have two separate inequalities:
-3x + 3 < 4
4 < -3x + 7.2
Solving the first inequality:
-3x < 1
Divide by -3 (remember to reverse the inequality sign since we're dividing by a negative number):
x > -1/3
Solving the second inequality:
4 < -3x + 7.2
-3x < 3.2
Divide by -3 (reverse the inequality sign):
x > -3.2/3
Combining the two inequalities, we have:
x > -1/3 and x > -3.2/3
To find the common range of values for x, we take the greater of the two lower bounds, which is x > -1/3.
Statement 2 alone is sufficient to determine a range for x, but it doesn't provide an exact value for x.
Considering both statements together:
From statement 1, we know that x < 19/5, which gives us an upper bound for x.
From statement 2, we know that x > -1/3, which gives us a lower bound for x.
Combining the information, we have:
-1/3 < x < 19/5
Therefore, with both statements together, we have a range for x but not an exact value.
The answer is option D: EACH statement ALONE is sufficient to answer the question asked.