2. SOLVING EQUATIONS Part 1 & 2 One Step and Two Step Equations Resources: Henrico County Schools – Algebra 1& Virginia Department of Education

3. One Step Equations Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

4. - 16 -16 r = -23 -23 + 16 = -7 Solve r + 16 = -7 1. Draw “the river” to separate the equation into 2 sides 2. Subtract 16 from both sides 3. Simplify vertically 4. Check your answer by substituting your answer back into the problem

5. When solving equations, we want to eliminate double signs. y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

6. Solve y + (-3) = 7 y – 3 = 7 + 3 +3 y = 10 10 + (-3) = 7 1.Draw “the river” to separate the equation into 2 sides 2.Eliminate the double sign 3.Add 3 to both sides 4.Simplify vertically 5.Check your answer by substituting your answer back into the problem

7. 3 · = 18 · 3 2x = 54 2 2 x = 27 1.Draw “the river” 2.Clear the fraction – multiply both sides by 3 3.Simplify 4.Divide both sides by 2 5.Simplify 6.Check your answer Solve = 18

8. To solve two-step equations, undo the operations by working backwards. Example: Ask yourself, 1. What is the first thing we are doing to x? 2. What is the second thing? Recall the order of operations as you answer these questions. Dividing by 2 Subtracting 3 To undo these steps, do the opposite operations in opposite order.

9. 1.Draw “the river” 2.Add 3 to both sides 3.Simplify 4.Clear the fraction - Multiply both sides by 2 5.Simplify 6.Check your answer Use a DO-UNDO chart as a shortcut to answering the questions. In the table, write the opposite operations in the opposite order DO UNDO ÷2 -3 Follow the steps in the ‘undo’ column to isolate the variable. + 3 + 3 = - 4 x = -8 -4 – 3 = -7 +3 · 2 2 · · 2

10. + 4 + 4 3 · · 3 x = 36 12 – 4 = 8 2) Solve 1. Draw “the river” 2. Add 4 to both sides 3. Simplify 4. Clear the fraction -Multiply both sides by 3 5. Simplify 6. Check your answer

11. 3) SOLVE d – 4 = 6 + 4 + 4 d = 10 1.Draw “the river” 2.Clear the fraction - Multiply both sides by 2 3.Simplify 4.Add 4 to both sides 5.Simplify 6.Check your answer

12. 4) Solve 1. d = -7 2. d = -19 3. d = -17 4. d = 17 Answer Now

13. 2(x+3) + 4x = 24 2x+6 +4x=24 2x+4x+6=24 6x+6=24 -6 -6 6x=18 6 6 X=3 Check 2(3+3)+4(3)=24 2(6)+ 12=24 12+12=24 24=24

14. Suggested Practice for SOL A.4 Students need additional practice solving multi-step equations with the variable on both sides and with fractions. Students also need additional practice justifying steps in solving a linear equation. Solve for x: What property justifies the work between each step? 13