Test Review One Step Equations

Focused on solving for the variable in each equation.

Importance of showing work and verifying answers through a check step.

Solving Individual Equations

Example 1: y + 3 = 18

• Step 1: Isolate variable - Subtract 3 from both sides:

  y + 3 - 3 = 18 - 3

  • Simplified: y = 15

• Check: - Substitute back into the original equation:

  15 + 3 = 18
  18 = 18

• Confirmed: correct answer.

Example 2: 4t = 16

• Step 1: Isolate variable - Divide both sides by 4:

  t = \frac{16}{4}

  • Simplified: t = 4

• Check: - Substitute:

  4(4) = 16
  16 = 16

• Confirmed: correct answer.

Example 3: j - 12 = 17

• Step 1: Add 12 to both sides - j - 12 + 12 = 17 + 12

  • Simplified: j = 29

• Check: - Substitute:

  29 - 12 = 17
  17 = 17

• Confirmed: correct answer.

Example 4: 3m = 48

• Step 1: Isolate variable - Divide both sides by 3:

  m = \frac{48}{3}

  • Simplified: m = 16

• Check: - Substitute:

  3(16) = 48
  48 = 48

• Confirmed: correct answer.

Example 5: b + 8.6 = 13

• Step 1: Isolate variable - Subtract 8.6 from both sides:

  b = 13 - 8.6

  • Simplified: b = 4.4

• Check: - Substitute:

  4.4 + 8.6 = 13
  13 = 13

• Confirmed: correct answer.

Example 6: 2b = 16

• Step 1: Isolate variable - Divide both sides by 2:

  b = \frac{16}{2}

  • Simplified: b = 8

• Check: - Substitute:

  2(8) = 16
  16 = 16

• Confirmed: correct answer.

Example 7: 7.5 + c = 16

• Step 1: Isolate variable - Subtract 7.5 from both sides:

  c = 16 - 7.5

  • Simplified: c = 8.5

• Check: - Substitute:

  7.5 + 8.5 = 16
  16 = 16

• Confirmed: correct answer.

Example 8: d - 5 = 20

• Step 1: Add 5 to both sides - d - 5 + 5 = 20 + 5

  • Simplified: d = 25

• Check: - Substitute:

  25 - 5 = 20
  20 = 20

• Confirmed: correct answer.

Example 9: 9x = 81

• Step 1: Isolate variable - Divide both sides by 9:

  x = \frac{81}{9}

  • Simplified: x = 9

• Check: - Substitute:

  9(9) = 81
  81 = 81

• Confirmed: correct answer.

Writing and Solving Word Problems

Situation 1: Ms. Lnenicka and Mr. Kent's Chickens

• Ms. Lnenicka has 16 chickens. She has 9 more than Mr. Kent.

• Let K = Mr. Kent's chickens.

• Equation:
  K + 9 = 16

• Step 1: Solve for K - Subtract 9 from both sides:

  K = 16 - 9

  • Simplified: K = 7

Situation 2: Solving for x

• Given equation: x + 6 = 23

• Step 1: Isolate variable

  • Subtract 6 from both sides:
    x = 23 - 6

  • Simplified: x = 17

• Determine value for (x - 10)

  • Compute: 17 - 10 = 7

Situation 3: Multiplication Problem (Ms. Hahn's Pasta)

• Ms. Hahn bought 5 boxes of pasta for $12.50.

• Let c = cost of a pasta box.

• Equation:
  5c = 12.50

• Step 1: Isolate variable - Divide both sides by 5:

  c = \frac{12.50}{5}

  • Simplified: c = 2.50

• Check: - Substitute:
  5 \times 2.50 = 12.50

  • Confirmed: correct answer.

Situation 4: Hot Chocolate Spills Challenge

• There were a total of 129 spills, with 3 spills per cup of hot chocolate.

• Let h = cups of hot chocolate.

• Equation:
  3h = 129

• Step 1: Solve for h - Divide both sides by 3:

  h = \frac{129}{3}

  • Simplified: h = 43

• Final Answer: 43 cups of hot chocolate.

Situation 5: Alex's Apples

• Alex has a total of 30 apples, which is 5 more than twice what Bob has.

• Let B = Bob's apples.

• Equation:
  2B + 5 = 30

• Step 1: Solve for B - Subtract 5 from both sides:

  2B = 30 - 5

  • Simplified: 2B = 25

• Step 2: Divide by 2 - B = \frac{25}{2}

  • Simplified: B = 12.5

Conclusion

• Practice solving one-step equations for mastery.

• Real-world situations can be modeled using simple equations to form connections between mathematical concepts and everyday scenarios.