Explanation: "Solving an equation" means to find the value of the variable that makes the equation true. For an equation such as 22 - x = 15, you can think of the algebraic equation in terms of "money". The equation can represent that you had $22, then spent some money and now have $15, so how much money did you spend? You may approach the problem using addition, such as 'counting up' from $15 to $20, which is $5, then from $20 to $22, which is $2. Since 5 + 2 = 7 then x = 7. You can approach the problem with subtraction. Since 22 - x = 15, then 22 - 15 = x, so x = 7.

Examples:

38 - x = 13 1st method: Counting up from 13 to 20 is 7 and counting up from 20 to 38 is 18. Since 7 + 18 = 25, x = 25. 2nd method: Since 38 - x = 13, then 38 - 13 = x. Therefore, x = 38 - 13, which is 25, so x = 25.

65 - x = 42 1st method: Counting up from 42 to 50 is 8 and counting up from 50 to 65 is 15. Since 8 + 15 = 23, x = 23. 2nd method: Since 65 - x = 42, then 65 - 42 = x. Therefore x = 65 - 42, which is 23, so x = 23.

Directions: For each problem in this problem set you will need to solve the equation using either method. Challenge yourself to be able to use each method. Strive to be able to accomplish each problem with ease and then strive for speed. Good luck and enjoy the challenge!