I need to solve for x
2x + 7 < x-4
Step 1: What does it mean? The left side (2x+7) is less than the right side (x-4). Now you have to find what value of x continues to make this expression true. You can do this in your head by the just guessing a number and plugging it in to "x". But this will take you a long time since you don't even know if "x" is a whole number or a fraction. This is where algebra comes into play!
Step 2: Algebra
2x+7 < x-4
Note the like terms. "2x" and "x" are like terms in the equation. "7" and "4" are a set of like terms that are different from the set containing "2x" and "x" because they don't possess a variable, instead they are whole numbers. We have to add the like terms together to solve. You'll see shortly with the steps that we will indeed solve the problem if we go this way.
Think about "<" as an equal sign. Each like term is separated from its pair and is on the other side of the "<" sign. So whenever that happens in Algebra and you want to add the like terms, this is how you do it.
2x+7 < x-4
-7 < -7
which is essentially: 2x < x-11
Now you want to bring the "x" on the right side over to the left side, so you have one set on one side and another set on another side. This way you can have the following expression:
2x < x + 3
x < -11 Your Answer
This means that any number chosen below -11 (and notice not exactly -11 because this is a less than expression and not a "less than or equal to") will satisfy the former equation: 2x + 7 < x-4
Try it for yourself!
Note that any number less than -11 could include -11.1 or -12 or anything smaller. Remember than unlike positive numbers, the farther a negative number is from 0 the smaller it is. Use the analogy that if you have $200 in the bank, you are rich and you are a big person. But if instead you have -$200 in your bank, you OWE the bank $200 dollars. If this -$200 were to change to -$1000, then you owe the bank $1000 ! So you are even poorer than before (analogy: when comparing to negative numbers, you're even smaller person than before).