six times the sum of 1 and some number is -6. what is the number?

Answer 1

In this case we will call "a number" x as it is unknown. We are given that 6 times the sum of a number and -1 is -6. the language here is key. the sum means addition, and the word "is" means equal. Therefore we need to set up an equation to solve for x. Here is that equation:

6(x + -1) = -6.

Multiply 6 with both terms in parentheses as a first step: 6*x + 6*-1 = -6. This gives us 6x - 6 = -6.

Then add six to both sides: 6x = 0.

Then divide both sides by 6: 6x/6 = 0/6

x = 0. In terms of solutions this is quite easy, using the zero property formulas/axioms. Any number times zero equals zero. So there it is! More wordy than most tutors but hence it works.

Answer 2

The first step for doing this is to write out the equation that represents that sentence:

6(1+x)=-6

Next, you want to do everything you can to isolate the x in stages remembering first to take care of what is outside of the parenthesis. Some tips: multiplication undoes division, division undoes multiplication, subtraction undoes addition (and visa versa). Therefore first we want to move the 6 that is multiplying (1+x) to the right side so we use division. Then we are left with 1+x=-1. Can you figure out what you would do next keeping in mind that the 1 is ADDED to the x so to undo that you would need to...?