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

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txmedteach eNotes educator| Certified Educator

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)`


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!):


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:


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:


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:



Now, we can add 42x to both sides:

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


Almost there, we can now divide by 2:

`2x/2 = 216/2`


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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