Solve for X in the Equation 7x + 5.5 = 19.5: Linear Equation Practice

Linear Equations with Decimal Constants

Solve the equation

7x+5.5=19.5 7x+5.5=19.5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We want to isolate the unknown X
00:10 Let's arrange the equation so that one side has only the unknown X
00:21 Let's group terms
00:27 Let's isolate the unknown X and calculate
00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the equation

7x+5.5=19.5 7x+5.5=19.5

2

Step-by-step solution

To solve the given equation 7x+5.5=19.5 7x + 5.5 = 19.5 , we'll follow these steps:

  • Step 1: Eliminate the constant term from the left side by subtracting 5.5 from both sides of the equation.
  • Step 2: Simplify the equation after subtraction to isolate the term with x x .
  • Step 3: Use division to solve for x x .

Now, let's work through each step:

Step 1: Subtract 5.5 from both sides.

We have:
7x+5.55.5=19.55.5 7x + 5.5 - 5.5 = 19.5 - 5.5

This simplifies to:
7x=14 7x = 14

Step 2: Divide both sides by 7 to solve for x x .

So, we divide by 7:
7x7=147 \frac{7x}{7} = \frac{14}{7}

This simplifies to:
x=2 x = 2

Therefore, the solution to the problem is x=2 x = 2 .

3

Final Answer

x=2 x=2

Key Points to Remember

Essential concepts to master this topic
  • Isolation Strategy: Subtract constant terms first to isolate the variable term
  • Step-by-Step: 7x + 5.5 - 5.5 = 19.5 - 5.5 gives 7x = 14
  • Verification: Substitute x = 2: 7(2) + 5.5 = 14 + 5.5 = 19.5 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing by the coefficient before eliminating constants
    Don't divide 7x + 5.5 = 19.5 by 7 first = messy fractions like x + 5.5/7 = 19.5/7! This creates unnecessary decimal complications. Always subtract or add constants first to isolate the variable term.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

\( x - 3 + 5 = 8 - 2 \)

FAQ

Everything you need to know about this question

Why do I subtract 5.5 from both sides instead of dividing by 7 first?

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Subtracting constants first isolates the variable term (7x), making division cleaner. If you divide first, you get messy fractions that are harder to work with!

What if I accidentally add 5.5 instead of subtracting it?

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Adding 5.5 would give you 7x+11=19.5 7x + 11 = 19.5 , leading to the wrong answer. Remember: to eliminate a positive constant, you must subtract it from both sides.

How do I know which operation to use first?

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Follow the reverse order of operations! Since addition/subtraction come last in PEMDAS, undo them first. Then handle multiplication/division.

Can I check my answer a different way?

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Yes! You can also work backwards: if x = 2, then 7(2) = 14, and 14 + 5.5 = 19.5. This confirms your solution is correct!

What if my final answer is not a whole number?

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That's completely normal! Linear equations often have decimal or fractional solutions. Just make sure to substitute back and verify your answer.

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