identify an integer x for which 2x/5 represents a ratio greater that 2:1 but less than 3:1
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To find an integer value of x for which 2x/5 represents a ratio greater than 2:1 but less than 3:1, we need to determine the range of values that satisfy these conditions.
First, let's set up the inequality for the given ratios:
2:1 < 2x/5 < 3:1
Next, let's convert the ratios to fractions:
2/1 < 2x/5 < 3/1
Simplifying the fractions:
2 < (2x/5) < 3
To get rid of the fraction, we can multiply all three sides of the inequality by 5:
5 * 2 < 5 * (2x/5) < 5 * 3
10 < 2x < 15
Now, let's solve the inequality:
10 < 2x < 15
Divide all sides of the inequality by 2:
10/2 < (2x/2) < 15/2
5 < x < 7.5
Since we're looking for an integer value of x, we can conclude that the possible values for x are 6 and 7. Any integer value of x within this range will satisfy the conditions, making 6 and 7 the suitable answers.