Identifying Equivalent Linear Expressions

Question

Which expression is equivalent to 7(6x)?

Answer 1

This is one of the more basic questions in algebra 1. We are just looking to determine the equivalent of a particular linear expression.

In This case, 7(6x) is also equal to 42x. The reason is fairly straightforward. Any item included within the parentheses is an item that is to be multiplied by the outside number. In this case, since (6x) is inside the parentheses, we simply multiply 6x times 7. 6 times 7= 42, and so we know the equivalent expression is 42x.

One of the great things about Algebra is that there is almost always more than one way to arrive at an answer. For those who struggle with direct multiplication in a scenario like this, you can solve doing simple addition. As long as you remember that (6x) needs to be multiplied by the outside number, you can simply add everything up.

In other words, 6x + 6x + 6x + 6x + 6x + 6x + 6x = 42x. You can even break down the addition further, though I would advise students to be hesitant on this, because the equations will only become more complex going forward.

Answer 2

6x * 7 = 42

6*7=42 the bring down the X

We can also expand this using addition to demonstrate what is happening here.

6x + 6x + 6x + 6x + 6x + 6x + 6x = 42x

If you were to count the number of times 6x was added there is a total of 7times.

The variable x remains the same in this instance because x is not being multiplied by any other variable, additionally, we do not know the value of X. Therefore, we write this answer as 42x. If we knew the value of x we could continue to solve however, since we do not we stop at this point.