Solve equations: complete the solution

What Does “Complete the Solution” Mean?

Sometimes an equation is partially solved or has missing steps.

“Complete the solution” means:

• Continue solving from where it is left off.
• Write all steps clearly until you find the value of the variable.
• Check the solution by substituting back into the original equation.

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Key Steps

• Identify the current step given in the question.
• Use inverse operations to isolate the variable.
• Perform operations on both sides (maintain the balance).
• Simplify each step.
• Write the final answer for the variable.
• Verify by substituting into the original equation.

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Example Problems

Example 1

Equation: 3x+4=13
Given Step: 3x=9

Complete the Solution:

• Divide both sides by 3:
  x=9/3
• Simplify:
  x=3

✅ Final Answer: x=3
🔍 Check: 3(3)+4=13 ✔

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Example 2

Equation: 5x−7=18
Given Step: 5x=25

Complete the Solution:

• Divide both sides by 5:
  x=25/5
• Simplify:
  x=5

✅ Final Answer: x=5
🔍 Check: 5(5)−7=18 ✔

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Example 3

Equation: 2(x+4)=20
Given Step: x+4=10

Complete the Solution:

• Subtract 4 from both sides:
  x=6

✅ Final Answer: x=6
🔍 Check: 2(6+4)=20✔

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Common Mistakes to Avoid

• Forgetting to do the same operation on both sides.
• Stopping before reaching the variable alone.
• Not checking the answer in the original equation.
• Ignoring negative signs.

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Practice Problems

Complete the solutions for the following equations:

1. 4x+5=21
   Given Step: 4x=16
2. 7x−9=26
   Given Step: 7x=35
3. 3(x−2)=15
   Given Step: x−2=5
4. 9x+12=30
   Given Step: 9x=18
5. 6x−4=14
   Given Step: 6x=18

Learn with an example

let’s practice!