Learn to solve equations using addition and subtraction.

An equation is a math problem with an equal sign. The goal of an equation is to find out what number the letter actually is. In this case we would want to figure out what number x minus 7 gets an answer of 24. 24 = x – 7

Example 1: Guess and Check One way to determine what x is, is guess and check by plugging in a number to see if it works. * Write down the equation: x + 8 = 15 * We are going to try x = 5, 7, or 23 Plug 5 into x to see if it works x + 8 = 15 5 + 8 = 15 13 = 15 Does 13 equal 5? NO! So 5 is not solution.

Example 1 Continued Now use the same equation: x + 8 = 15 * We are going to try the next number from x = 5, 7, or 23 Plug 7 into x to see if it works x + 8 = 15 7 + 8 = 15 15 = 15 Does 15 equal 5? YES! So 7 is the solution! This means that when x + 8 = 15, x = 7

Example 2: Guess and Check Now you try it on your own! * Write down the equation: x – 4 = 25 * Try x = 21, 28, or 29 Plug 21 into x: Plug 28 into x: Plug 29 into x: x – 4 = 25 x – 4 = 25 x – 4 = 25 21 – 4 = 25 28 – 4 = 25 29 – 4 = 25 17 = 25 24 = 25 25 = 25 This means that when x – 4 = 25, x = 25

We are going to DO THE OPPOSITE of what is happening in the equation. Sometimes guess and check takes a little while to find the right number for the letter. We can SOLVE an addition or subtraction problem by doing the inverse operation. We are going to DO THE OPPOSITE of what is happening in the equation.

Example 3: Steps to Solve a One-Step Equation Step 1: Find the letter (n) Step 2: Find the number right next to the letter (10) Write 10 + n = 18 10 + n = 18 Step 3: Is the number next to the letter being added or subtracted? (added) Step 4: You need to do the OPPOSITE of that to the number, on both sides of the equation (subtract 10 from 10 and 18) 10 + n = 18 –10 –10 0 + n = 8 n = 8 Check: Step 5: Then the letter is the only thing left on one side and the correct number that works is on the other side (n = 8) Step 6: Check your answer by plugging in the answer to the problem (10+8=18) 10 + n = 18 10 + 8 = 18 18 = 18

Example 4: Solving One Step Equations Write p – 8 = 9 p – 8 = 9 Find the letter and the number next to it. The problem is subtracting, so we need to DO THE OPPOSITE, add Add 8 (the number next to the letter) to BOTH sides of the equation The letter will equal a new number Now take that number and plug it back into the equation The numbers should equal each other p – 8 = 9 + 8 + 8 p + 0 = 17 p = 17 Check: p – 8 = 9 17 – 8 = 9 9 = 9

Example 5: Solving One Step Equations Solve 22 = y – 11 C. 22 = y – 11 22 = y – 11 Subtraction problem, so add 11 to both sides. + 11 + 11 33 = y + 0 33 = y Check Plug your answer back into the equation to check it! 22 = y – 11 22 = 33 – 11 22 = 22

Example 6: Solving One Step Equations Solve 12 = y + 7 C. 12 = y + 7 12 = y + 7 Addition problem, so subtract 7 from both sides. - 7 - 7 5 = y + 0 5 = y Check Plug your answer back into the equation to check it! 12 = y + 7 12 = 5 + 7 12 = 12

= = + + Example 7: Story Problem Solve: 895 n 1125 895 + n = 1125 –895 B. From 1980 to 2000, the population of a town increased from 895 residents to 1125 residents. What was the increase in population during that 20-year period? initial population increase in population + = population after increase + = Solve: 895 n 1125 895 + n = 1125 –895 – 895 Subtract 895 from both sides. 0 + n = 230 n = 230 The increase in population was 230.

Partner Lesson Quiz 8 21 a = 18 n = 45 3.69 + n = 4.25; $0.56 Determine which value of x is a solution of the equation. 1. x + 9 = 17; x = 6, 8, or 26 2. x – 3 = 18; x = 15, 18, or 21 Solve. 3. a + 4 = 22 4. n – 6 = 39 5. The price of your favorite cereal is now $4.25. In prior weeks the price was $3.69. Write and solve an equation to find n, the increase in the price of the cereal. 8 21 a = 18 n = 45 3.69 + n = 4.25; $0.56