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One-Step Linear Equations

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One-Step Linear Equations worksheet preview
One-Step Linear Equations

One-Step Linear Equations

Balance scale showing equation solving

⚖️ Part 1: Understanding Balance in Equations

1. Circle the correct meaning of the equal sign (=):

The answer comes next

Both sides are balanced or the same

Add the numbers together

2. Which of these number sentences are true? Check all that apply:

3 + 5 = 4 + 4

7 + 2 = 10 - 1

6 × 2 = 15 - 3

8 + 4 = 20 ÷ 2

3. In the equation x + 5 = 12, what does the letter x represent?

🔢 Part 2: Solving Addition and Subtraction Equations

4. Solve these equations by using inverse operations. Show your working:

a) x + 7 = 15

b) y + 3 = 11

c) m - 4 = 9

d) n - 6 = 2

5. Check your answer for question 4a by substituting x = 8 back into the original equation:

✖️➗ Part 3: Solving Multiplication and Division Equations

6. Solve these equations using inverse operations. Show your working:

a) 3x = 21

b) 5y = 35

c) z ÷ 4 = 6

d) w ÷ 3 = 8

🎯 Part 4: Equation Matching Challenge

7. Match each equation with its correct solution by drawing lines:
1. x + 8 = 15
2. y - 5 = 12
3. 4z = 28
4. m ÷ 6 = 3
5. n + 9 = 20
A. z = 7
B. n = 11
C. x = 7
D. m = 18
E. y = 17

🧠 Part 5: Word Problems

8. Write and solve an equation for each word problem:

a) Sarah had some stickers. She gave away 8 stickers and now has 15 left. How many stickers did she start with?

Equation: ________________

b) A packet of lollies costs $3. Jake bought some packets and spent $21 in total. How many packets did he buy?

Equation: ________________

9. True or False? Circle your answer and explain your reasoning:

The equation x - 7 = 12 has the same solution as x = 12 + 7

True

False

Explanation: ________________________________________________

💭 Part 6: Reflection

10. Fill in the blanks to complete these important facts about solving equations:

To solve x + 5 = 12, I need to __________ 5 from both sides because subtraction is the __________ operation of addition.

To solve 3y = 15, I need to __________ both sides by 3 because division is the __________ operation of multiplication.

11. Explain in your own words what it means for an equation to be "balanced":
12. What is one strategy you can use to check if your solution to an equation is correct?

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