# -40x+45=3[7-2(7x-40] Can you solve this problem?

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### 1 Answer

This problem is a standard "Solve for x" problem that we so often see in algebra. I'm going to rewrite it below to get everything in a good font:

`-40x+45 = 3(7-2(7x-40))`

To do this equation most easily, we're going to have to simplify the term on the right. To do this we'll need to use the **distributive property** (see link). Here's an example of that:

`a(b+c) = ab + ac`

Whenever we're multiplying numbers in parentheses by another number, we're "distributing" it to each term inside the parentheses.

In our equation, we're going to "distribute" the 3 outside the parentheses to the terms inside the parentheses:

`-40x+45 = 3(7-2(7x-40))`

`-40x+45 = 3*7-3*2(7x-40)`

`-40x+45=21-6(7x-40)`

We can do the same with the 6 on the right side seen here (don't forget to distribute the -1! This makes it a + on that third term!):

`-40x+45=21-6*7x+6*40`

Keep in mind, we're only multiplying the 6by the terms inside its adjacent parentheses. We aren't multiplying it by the 21, for this reason.

Let's simplify:

`-40x+45=21-42x+240`

We can combine "like" terms now, meaning we can combine numbers with other numbers on the same side and terms with x with other terms of x on the same side. In our case, the only "like" terms we'll be combining are 21 and -240:

`-40x+45=-42x+261`

Now, we are in a good position to isolate the *x * and solve the equation. First, we're going to subtract 45 from both sides:

`-40x+45-45=-42x+261-45`

`-40x=-42x+216`

Now, we can add 42x to both sides:

`-40x + 42x = -42x+216+42x`

`2x=216`

Almost there, we can now divide by 2:

`2x/2 = 216/2`

`x=108`

And there's your answer! Now, you can substitute 108 for x in the original equation and check to make sure both sides are equal, which they are. Hope that helps!

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