7/11 - 2x < 3/10; {1/2, 1/3, 1/4, 1/5, 1/6}
Rearrange the inequality to get
add 2x to both sides
7/11 < 3/10 +2x
subtract 3/10 from both sides
7/11 - 3/10 < 2x
divide by both sides 2
(1/2)(7/11 - 3/10) < x
Can you finish it out?
Certainly! Let's continue solving the inequality:
(1/2)(7/11 - 3/10) < x
To simplify the expression inside the parentheses, we need to find a common denominator for 11 and 10, which is 110. Then, we can rewrite 7/11 and 3/10 with denominators of 110:
(1/2)((7 * 10)/(11 * 10) - (3 * 11)/(10 * 11)) < x
(1/2)((70/110) - (33/110)) < x
Now, we can subtract the fractions inside the parentheses:
(1/2)(37/110) < x
To calculate (1/2)(37/110), we multiply the numerators and denominators:
(1 * 37)/(2 * 110) < x
37/220 < x
So, the inequality simplifies to:
37/220 < x
Now, let's check which of the given fractions {1/2, 1/3, 1/4, 1/5, 1/6} satisfy the inequality. We can compare each fraction with 37/220 to see if it is less than x:
1/2 < 37/220? No
1/3 < 37/220? No
1/4 < 37/220? No
1/5 < 37/220? No
1/6 < 37/220? Yes
Therefore, the solution to the inequality 7/11 - 2x < 3/10 is:
x > 1/6