Let’s Review -- An equation is similar to a scale. Both sides of the scale need to be equal in order for the scale to balance. Properties of equality says that I can add, subtract, multiply and divide the same number to each side of the equation and it will be true.

So to solve this equation, I will subtract 2 from each side (keeping the equation equal). It looks like this equation has a solution of 3. We don’t know if it really is a solution until we try it. So, let’s replace 3 for x. When we do that 3+2=5, 5=5 so 3 is a solution.

In order to make sure that you combine like terms, you need to understand what like terms are. A term is each single part of an expression. They are connected to each other through addition and subtraction. Like terms would be terms that have the same variable. Constants, which are numbers on their own, are like terms. Coefficients are the numbers in front of a variable. They represent the number used to multiply the variable. So in the expression 2x + 7 + 4x – 2 – 5y, the like terms would be 2x and 4x and 7 and -2. Combining like terms helps us to simplify expressions or equations. The resulting simplified expression would be: 6x+5-5y. Combining like terms does not change the value of the expression, so it doesn’t change the solution to the equation. Also, combining like terms is not a requirement for solving, but is helpful in writing the equation in a form that we can work with more easily.

When we look at this equation, we notice that there are like terms on the left hand side of the equation. If we combine these like terms, we get 5x = 45. Using the division property of equality, we can divide both side of the equation by 5. Giving us x = 9. When we check our solution by using the substitution property of equality, we see that 9 makes the equation true, so it is a solution for the equation.

We found that x = 9 in the equation 2x + 3x =45 We found that x = 9 in the equation 2x + 3x =45. Is it also a solution for the equation when the terms are combined? Let’s see. When we put x = 9 into 2x + 3x = 45, we see that it is a solution to the equation because 45 = 45. Both sides of the equation are equal, so 9 is a solution. Now let’s put 9 in for x in the equation that combined like terms. When we combine 2x + 3x, we get 5x. Now, let’s substitute 9 into 9. When we simplify, we get 45 = 45. So 9 makes this equation true. This shows us that the original equation and the equation with like terms combined are equivalent.

-7(- 27 7 ) -5 + 2 = 24 x= - 27 7 In this equation, we notice that there are like terms on the left hand side of the equation. These like terms are constants. If we combine these like terms, we get -7x – 3 = 24. Using the addition property of equality, we can add 3 to both sides of the equation giving us -7x = 27. We can use the division property of equality and divide both sides by -7. Our solution is -27/7. When we check our solution by using the substitution property of equality, we see that -27/7 makes the equation true, so it is a solution for the equation. As you can see, combining like terms allows us to make solving an equation easier and simpler.

-7(- 12 5 ) -5 + 2 = 24 84 5 – 5 + 2 = 24 x= - 24 10 =- 12 5 We found that -27/7 was a solution to the equation -7x-5+2=24. What happens if I combine unlike terms? Instead of adding just -5 and 2, I am going to pretend that all three terms are like. We know they are not like terms because they do not contain the same variable. But to show you what happens when we combine unlike terms, we are going to combine all of these terms. So the mistake is add -7x,-5, and +2 to get -10x = 24. Do using the division property of equality, we can divide by -10 and x = -24/10 or -12/5. We always want to substitute our answer into the original equation in case we make a mistake. Remember…we didn’t not combine like terms, we combined all terms incorrectly. So let’s substitute -12/5 in for x in -7x-5+2 = 24. After we multiply -7 time -12/5 subtract 5 and add 2, we get 13.8 = 24. We know that -12/5 cannot be solution to the equation, so we made a mistake somewhere. And in our case it was when we combined liked terms.

The solution for 2x – 7 + 3 = 12 is? a) 4 b) 1 c) -1 d) -4 The solution for 4 – 5x+ 1 = 10 is? a) 1 b) 2 c) -2 d) -1