1) When adding like terms with the same variable exponent, you add the coefficients and keep the same exponent, not change the exponent. x + x = 2x, not x^2. 2) Terms are only like terms if they have the same variables raised to the same exponents. 3x + 2 cannot be simplified to 5x since x and 3 are not like terms. 3) When distributing, you must distribute to each term in the parentheses. 2(3x - 5) = 6x - 10, not 6x - 5. 4) Be careful of signs and what number the variable is being added or subtracted to. x + 3 = -4 becomes x = -

3. Common Error #1:
x+x =x 2

4. Remember when adding and subtracting,
do not mess with the exponents!
x + x ≠ x2
x + x = 2x

5. Common Error #2
3x + 2 =
5x

6. Remember: x2, x, and 3 are not like terms.
Thus, 3x + 2 ≠ 5x
3x + 2 = 3x + 2
It cannot be simplified!

7. Common Error #3:
2(3x – 5) = 6x - 5

8. Distributive property means to distribute to each term in
the parenthesis! Thus, 3(2x – 5) ≠ 6x - 5
3(2x – 5) = 6x - 15

9. Common Error #4
x + 3 = -4
+4 +4
x =7

10. If calculated properly: x + 3 = -4
+ 4 +4
x+7=0
Pay attention to the x on the left side. What number is in the way?
x + 3 = -4
- 3 -3
x = -7

11. Common Error #5
-3 2 =9

12. The base of the exponent is 3, not -3
Thus, -32≠ 9
-32 = -(3)(3) = -9
(-3) 2 = (-3)(-3) = 9