twice the sum of a number and 5 is the same as two less than six times the same number.find the number

Answer 1

Hello Jackie,

First, let's come up with some expressions to represent the information given in the problem, fair enough? Doing so will allow us to create an equation which we can then solve.

2(x + 5) = 6x - 2 <-------twice the sum of a number and 5 is the same as two less than six times the same number.

2(x +5) = 6x - 2 <------Using the distributive property on the left side

2x + 10 = 6x - 2 <-------Subtract 2x and add 2 to both sides of the equation

12 = 4x <-------When performing the above functions, this is what you end up with.

4x = 12 <------ Simply switching sides

x = 3 <-------This is the number

Next, let's substitute 3 for x in the original equation to check our work, fair enough?

2(3 + 5) = 6(3) - 2

6 + 10 = 18 - 2

16 = 16

The solution checks out and is therefore valid and correct. I hope this assists and that you have a Happy Holiday Season. If you have further questions regarding this solution, have feedback, or need clarity, please just click the "add comment" button and type whatever you wish or need to convey. If you need one on one tutoring, please feel free to reach out to me or any tutor. Best!