Question

Find the largest number such that if |x - 2| < 0.1, then |2x - 4| < ?

Answer 1

To find the largest number such that if |x - 2| < 0.1, then |2x - 4| < ?, we need to determine the largest value of |2x - 4| that satisfies the condition |x - 2| < 0.1. The largest possible value for |2x - 4| is 0.8.

Step-by-step explanation:

To find the largest number such that if |x - 2| < 0.1, then |2x - 4| < ?, we need to determine the largest value of |2x - 4| that satisfies the condition |x - 2| < 0.1.

Let's set up the inequalities:

• |x - 2| < 0.1
• 0 < x - 2 < 0.1
• 2 < x < 2.1

Substituting the values into the second inequality, we find that the largest value of x that satisfies the condition is x = 2.1.

Now, let's substitute this value into |2x - 4| to find the largest possible value:

• |2(2.1) - 4| = |-0.8| = 0.8

Therefore, the largest possible value for |2x - 4| is 0.8.