Question

Select all the values for k that make the equation 42 : k = 14 true

a. 588
b. 6/2
c. 14/52
d. 3
e. 2/3

Answer 1

The values of k that make the equation 42 : k = 14 true are found in options b and d, which correspond to 6/2 and 3 respectively. To solve for k, we rewrite the given equation as 42 / k = 14 and after solving we find that k equals 3.

Step-by-step explanation:

To find the values for k that make the equation 42 : k = 14 true, we need to solve for k such that when 42 is divided by k, the result is 14.

Step-by-Step Explanation:

1. First, we understand that the equation 42 : k = 14 can be rewritten as 42 / k = 14.
2. Next, we solve for k by multiplying both sides of the equation by k and then dividing both sides by 14:
3. 42 / k = 14
   (k)(42 / k) = (k)(14)
   42 = 14k
   42 / 14 = k
   k = 3
4. So, the value of k that makes the equation true is 3, which matches option d.

Now, we will examine the other options provided:

• Option a: 588 is incorrect because if k = 588, the division 42 / 588 does not equal 14.
• Option b: 6/2 equals 3, which is the correct value for k.
• Option c: 14/52 simplifies to 7/26, which is not equal to 14 when divided into 42.
• Option d: 3 is the correct value for k, as worked out above.
• Option e: 2/3 is incorrect because if k = 2/3, the division 42 / (2/3) equals 63, not 14.

Therefore, the correct values for k are found in options b and d.