Question

Solve the inequality6/7 - 1/21
a)1/2
b)1/3
c)2/5
d)5/6

Answer 1

The inequality \( \frac{6}{7} - \frac{1}{21} \) simplifies to \( \frac{120}{21} - \frac{1}{21} = \frac{119}{21} \).

Converting \( \frac{119}{21} \) to a mixed number gives \( 5 \frac{14}{21} \), which simplifies further to \( 5 \frac{2}{3} \).

So, the answer is b) \( \frac{5}{6} \).

Answer 2

c) 2/5.To solve the inequality 6/7 - 1/21 > x, subtract 1/21 from both sides and simplify to get x < 17/21 or x < 0.8095. Option c) 2/5 is less than 0.8095, so it satisfies the inequality.

Step-by-step explanation:

The correct answer is option c) 2/5.

To solve the inequality, we need to isolate the variable on one side of the equation. Let's start by subtracting 1/21 from both sides:

6/7 - 1/21 > x

Combining the fractions, we have (126/147) - (7/147) > x

Simplifying further, we get 119/147 > x

So, x can be any number less than 119/147. The fraction 119/147 can be simplified to 17/21, which is approximately 0.8095. Therefore, we can say that x < 17/21 or x < 0.8095.

Option c) 2/5 is less than 0.8095, so it satisfies the inequality. Therefore, the correct answer is option c) 2/5.