Question

question 2 of 5
select the correct answer.
the sum of 2 times a number and 10 is the same as 6 times the difference of the number and 1. what is the number?
-4
-1
1
4

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

The sum of 2 times the number and 10 is \( 2x + 10 \).
6 times the difference of the number and 1 is \( 6(x - 1) \).
Since they are the same, we have the equation: \( 2x + 10 = 6(x - 1) \)

Step3: Solve the equation

First, expand the right - hand side: \( 2x+10 = 6x-6 \)
Then, subtract \( 2x \) from both sides: \( 10=6x - 2x-6 \), which simplifies to \( 10 = 4x-6 \)
Next, add 6 to both sides: \( 10 + 6=4x \), so \( 16 = 4x \)
Finally, divide both sides by 4: \( x=\frac{16}{4}=4 \)

Answer:

4 (the option: 4)