Question

How do you solve `7(10-3w)=5(15-4w)`?

Answer 1

`w = -5`

Explanation:

Firstly, to solve the equation we must expand it so the numbers are therefore easier to work with.

If you are unsure how to expand an equation, we must multiply the number(s) outside the bracket by the numbers within the bracket.

This will give us,

`7 xx 10 + 7 xx (-3w) = 5 xx 15 + 5 xx(-4w)`

`70 -21w = 75 - 20w`

As you asked, you would like to solve the equation, so firstly we must recognize that this equation has two sides. We must rearrange the equation to have a number on one side, with an equation on the other

To do so, we need to take our smallest like term with a figure to the opposing side. This will leave us with a number on one side.

The smallest figure is `-21w`, so we must move it to the other side. When we move numbers to the other side, we then change it to the opposite sign, giving us `+21w`.

`70 = 75 - 20w +21w`

Collecting out two like terms to get the equation,

`70 = 75 + w`

We can now work it out. I don't know about you but I find it easier to work out my answer when the answer number is on the right hand side, and letter is on the far left which I will do

`75 + w = 70`

can also be written as

`w + 75 = 70`

Now we must do the inverse, subtract `75` from both sides, since it is a positive number

`w + 75 = 70`

`w = 0 + -5`

`w = -5`

Our answer is, therefore:

`w = -5`