Solve the Linear Equation: What is X in 10 + 9x = 91?

Linear Equations with Single Variable Terms

10+9x=91 10+9x=91

How much is X worth?

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Step-by-step video solution

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00:00 We want to isolate the unknown - subtract 10 from both sides
00:22 We'll divide by 9 to know what one unknown equals

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

10+9x=91 10+9x=91

How much is X worth?

2

Step-by-step solution

To solve the equation 10+9x=91 10 + 9x = 91 , we'll follow these steps:

  • Step 1: Eliminate the constant term on the left side by subtracting 10 from both sides of the equation.

10+9x10=9110 10 + 9x - 10 = 91 - 10 9x=81 9x = 81

  • Step 2: Solve for x x by dividing each side of the equation by the coefficient of x x , which is 9.

9x9=819 \frac{9x}{9} = \frac{81}{9} x=9 x = 9

Hence, the value of x x is 9 9 .

3

Final Answer

9 9

Key Points to Remember

Essential concepts to master this topic
  • Isolation Rule: Remove constants first, then divide by the coefficient
  • Technique: Subtract 10 from both sides: 91 - 10 = 81
  • Check: Substitute back: 10 + 9(9) = 10 + 81 = 91 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing before subtracting the constant
    Don't divide 91 by 9 first = 10.11, then subtract 10! This ignores order of operations and gives a decimal answer when the solution should be a whole number. Always eliminate constants first, then handle coefficients.

Practice Quiz

Test your knowledge with interactive questions

\( x+7=14 \)

\( x=\text{?} \)

FAQ

Everything you need to know about this question

Why do I subtract 10 from both sides instead of dividing by 9 first?

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You need to isolate the term with x first! Think of it like unwrapping a gift - you remove the outer layer (the constant +10) before getting to the inner layer (the coefficient 9).

What if I get a negative number when subtracting?

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That's completely normal! If the constant on the left is larger than the number on the right, you'll get a negative result. Just continue with the steps - negative numbers follow the same rules.

How do I know which operation to do first?

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Follow the reverse order of operations! Since addition/subtraction come after multiplication/division in PEMDAS, you undo them first when solving equations.

Can I check my answer a different way?

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Yes! You can also think about it logically: "What number times 9, plus 10, equals 91?" Try different values until you find one that works, then verify with substitution.

What if my coefficient isn't a nice whole number?

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The same steps work! You might end up with fractions or decimals, but the process is identical: subtract constants first, then divide by the coefficient.

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