Solving TwoStep Equations You will solve equations by
Solving Two-Step Equations You will solve equations by undoing operations using properties of equality. Essential Question: How do you solve two-step equations? TP: Construct and solve two step equations for real world problems by combining like terms
Steps for Solving Two-Step Equations 1. Solve for any Addition or Subtraction on the variable side of equation by “undoing” the operation from both sides of the equation. Solve any Multiplication or Division from variable side of equation by “undoing” the operation from both sides of the equation. Inverse Operations Addition Subtraction Multiplication Division 2. Whatever the other you do to one side, you must do to side to keep property of equality.
Example 1: Solve 4 x – 5 = 15 4 x – 5 = +5 4 x = 4 x=5 Check: 15 +5 (Add 5 to both sides) 20 (Simplify) 4(Divide both sides by 4) (Simplify) 4(5) -5 =15 20 – 5 = 15 15 =15
EXAMPLE 2 Solve a two-step equation x + 5 = 11. 2 x + 5 = 11 2 x + 5 – 5 = 11 – 5 2 x =6 2 2 x =2 6 2 x = 12 Write original equation. Subtraction Property of Equality Simplify. Multiplication Property of Equality. Simplify. ANSWER The solution is 12. Check by substituting 12 for x in the original equation.
EXAMPLE 2 CHECK Solve a two-step equation x + 5 = 11 Write original equation. 2 12 + 5 ? = 11 Substitute 12 for x. 2 11 = 11 Simplify. Solution checks.
GUIDED PRACTICE for Example 1 &2 Solve the equation. Check your solution. 1. 5 x + 9 = 24 SOLUTION 5 x + 9 = 24 5 x + 9 – 9 = 24 – 9 5 x = 15 5 x 15 5 = 5 x=3 Write original equation. Subtraction Property of Equality Simplify. Division Property of Equality Simplify.
GUIDED PRACTICE for Example 1 ANSWER The solution is 3. Check by substituting 3 for x in the original equation. CHECK 5 x + 9 = 24 ? 5 3 + 9 = 24 24 = 24 Write original equation. Substitute 3 for x. Simplify. Solution check.
GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. 2. 4 y – 4 = 16 SOLUTION 4 y – 4 = 16 4 y – 4 + 4 = 16 + 4 4 y = 20 4 y 20 = 4 4 y=5 Write original equation. Addition Property of Equality Simplify. Division Property of Equality. Simplify.
GUIDED PRACTICE for Example 1 ANSWER The solution is 5. Check by substituting 5 for y in the original equation. CHECK 4 y – 4 = 16 ? 4(5) – 4 = 16 16 = 16 Write original equation. Substitute 5 for y. Simplify. Solution checks.
GUIDED PRACTICE for Example 1 Solve the equation. Check your solution. z 3. – 1 = 3 – 7 SOLUTION – 1= z – 7 3 z – 1+7= – 7+7 3 z 6= 3 z 3 6=3 3 18 = z Write original equation. Add 7 to each side. Simplify. Multiply each side by 3. Simplify.
GUIDED PRACTICE for Example 1 ANSWER The solution is 18. Check by substituting 18 for z in the original equation. CHECK z – 7 3 ? 18 – 1= – 7 3 – 1= Write original equation. Substitute 18 for z. Simplify. Solution checks.
EXAMPLE 3 Solve a two-step equation by combining like terms Solve 7 x – 4 x = 21 3 x = 21 3 3 x=7 Write original equation. Combine like terms. Divide each side by 3. Simplify.
GUIDED PRACTICE for Examples 3 Solve the equation. Check your solution. 5. 8 t – 3 t = 35 5 t = 355 5 t =7 Write original equation. Substract the like terms Divide each side by 5 Simplify.
GUIDED PRACTICE CHECK 8 t – 3 t = 35 8(7) – 3(7) =? 35 ? 56 – 21 = 35 35 =35 for Examples 3 Write original equation. Substitute 7 for t. Multiply. Simplify. Solution checks.
GUIDED PRACTICE for Example 4 Jobs 10. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work? SOLUTION 53 = 13 + 8 h 53– 13 = 13 – 13 + 8 h 40 = 8 h 5=h Write the equation Subtraction Property of Equality. Simplify. Division Property of Equality
GUIDED PRACTICE for Example 4 ANSWER She worked for 5 hours
How do you solve two-step equations? Essential Question:
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