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Solving Two-Step Equations

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

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Solving Two-Step Equations

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  1. Solving Two-StepEquations 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

  2. Steps for Solving Two-Step Equations • 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 Whatever you do to one side, you must do to the other side to keep property of equality.

  3. Example 1: Solve 4x – 5 = 15 4x – 5 = 15 +5 +5 (Add 5 to both sides) 4x = 20 (Simplify) 4 4 (Divide both sides by 4) x = 5 (Simplify) Check: 4(5) -5 =15 20 – 5 = 15 15 =15

  4. Solve + 5 = 11. 11 + 5 = + 5 – 5 = 11 – 5 x x x x x 6 = 2 2 2 2 2 x = 12 2 = 2 6 ANSWER The solution is 12. Check by substituting 12 for xin the original equation. EXAMPLE 2 Solve a two-step equation Write original equation. Subtraction Property of Equality Simplify. Multiplication Property of Equality. Simplify.

  5. 11 ? 12 + 5 = 11 + 5 = 2 11 11 =  x 2 EXAMPLE 2 Solve a two-step equation CHECK Write original equation. Substitute 12 for x. Simplify. Solution checks.

  6. 5x + 9 = 24 5x + 9 – 9 = 24 – 9 15 5x = = 15 5x 5 5 3 x = for Example 1 &2 GUIDED PRACTICE Solve the equation. Check your solution. 1. 5x + 9 = 24 SOLUTION Write original equation. Subtraction Property of Equality Simplify. Division Property of Equality Simplify.

  7. 5x + 9 = 24 ? 53 + 9 = 24 24 = 24 ANSWER The solution is 3. Check by substituting 3 for xin the original equation. for Example 1 GUIDED PRACTICE CHECK Write original equation. Substitute 3 for x. Simplify. Solution check.

  8. 4y – 4 = 16 4y – 4 + 4 = 16 + 4 20 4y = 20 4y = 4 4 y = 5 for Example 1 GUIDED PRACTICE Solve the equation. Check your solution. 2. 4y – 4= 16 SOLUTION Write original equation. Addition Property of Equality Simplify. Division Property of Equality. Simplify.

  9. 4y – 4 = 16 ? 4(5) – 4 = 16 16 = 16 ANSWER The solution is 5. Check by substituting 5 for yin the original equation. for Example 1 GUIDED PRACTICE CHECK Write original equation. Substitute 5 for y. Simplify. Solution checks.

  10. 3. – 1 = –7 – 1 = – 7 z z z z z – 1 + 7 = – 7 + 7 3 3 3 3 3 6 = 3 6 = 3 z 18 = for Example 1 GUIDED PRACTICE Solve the equation. Check your solution. SOLUTION Write original equation. Add 7 to each side. Simplify. Multiply each side by 3. Simplify.

  11. – 1 = – 7 z ? 18 3 – 1 = – 7 3 – 1 = – 1 ANSWER The solution is 18. Check by substituting 18 for zin the original equation. for Example 1 GUIDED PRACTICE CHECK Write original equation. Substitute 18 for z. Simplify. Solution checks.

  12. = 3x 21 3 3 EXAMPLE 3 Solve a two-step equation by combining like terms Solve7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide each side by 3. x = 7 Simplify.

  13. 5t 35 5 = 5 for Examples 3 GUIDED PRACTICE Solve the equation. Check your solution. 5. 8t – 3t = 35 8t – 3t = 35 Write original equation. 5t = 35 Substract the like terms Divide each side by 5 t=7 Simplify.

  14. ? 8t– 3t= 35 CHECK 8(7) – 3(7) = 35 ? 56 – 21 = 35 for Examples 3 GUIDED PRACTICE Write original equation. Substitute7 fort. Multiply. 35=35 Simplify. Solution checks.

  15. for Example 4 GUIDED PRACTICE 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 + 8h Write the equation 53–13= 13 –13 + 8h Subtraction Property of Equality. 40 = 8h Simplify. 5 = h Division Property of Equality

  16. ANSWER She worked for 5 hours for Example 4 GUIDED PRACTICE

  17. How do you solve two-step equations? Essential Question:

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