Math Problem Statement

Solve the following equation for x: 12x + 6/11 - 5 = 0

Solution

The equation given in the image is:

12x+6115=012x + \frac{6}{11} - 5 = 0

To solve for xx, follow these steps:

  1. Combine like terms: 12x+6115=012x + \frac{6}{11} - 5 = 0 Move the constants to the other side of the equation: 12x=561112x = 5 - \frac{6}{11}

  2. To combine the constants on the right-hand side, convert 5 into a fraction with a denominator of 11: 5=55115 = \frac{55}{11} Now subtract the fractions: 5511611=4911\frac{55}{11} - \frac{6}{11} = \frac{49}{11} So, 12x=491112x = \frac{49}{11}

  3. Solve for xx by dividing both sides by 12: x=4911×112=49132x = \frac{49}{11} \times \frac{1}{12} = \frac{49}{132}

So, the solution is: x=49132x = \frac{49}{132}

Would you like more details on this solution or have any other questions?


Here are some follow-up questions to deepen your understanding:

  1. How can you verify the solution x=49132x = \frac{49}{132} by substituting it back into the original equation?
  2. What steps would you take if the equation had a variable in the denominator?
  3. How would you solve the equation if there was an additional term with xx on the right side?
  4. Can you think of a different approach to solve the equation, such as using decimal approximations?
  5. How would the solution process change if the equation included square roots or higher powers of xx?

Tip: When solving equations with fractions, it's often helpful to find a common denominator early on to simplify your calculations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Fraction Operations

Formulas

Operations with fractions
Solving linear equations ax + b = c

Theorems

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Suitable Grade Level

Grades 6-8