Solve the equation: 14x - 9 + 2x - 5 = 13x - 3 + 2x.

Question image

Understand the Problem

The question is asking to solve the equation given: 14x - 9 + 2x - 5 = 13x - 3 + 2x. The goal is to find the value of 'x'.

Answer

The value of $x$ is $11$.
Answer for screen readers

The value of $x$ is $11$.

Steps to Solve

  1. Combine like terms on the left side

For the left side of the equation, combine the $x$ terms and the constant terms:

$$ 14x + 2x - 9 - 5 = 16x - 14 $$

  1. Combine like terms on the right side

For the right side of the equation, combine the $x$ terms and the constant terms:

$$ 13x + 2x - 3 = 15x - 3 $$

  1. Set the combined equations equal to each other

Now we have the simplified equation:

$$ 16x - 14 = 15x - 3 $$

  1. Isolate the variable

Subtract $15x$ from both sides to isolate $x$:

$$ 16x - 15x - 14 = -3 $$

This simplifies to:

$$ x - 14 = -3 $$

  1. Solve for $x$

Now, add $14$ to both sides:

$$ x = -3 + 14 $$

This simplifies to:

$$ x = 11 $$

The value of $x$ is $11$.

More Information

The equation you started with is a linear equation, and solving it involves isolating the variable on one side. It's useful to rearrange and combine like terms to simplify the equation before solving.

Tips

  • Forgetting to combine like terms correctly, which can lead to an incorrect equation.
  • Misapplying the operations when isolating the variable; double-check each step for arithmetic mistakes.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!
Use Quizgecko on...
Browser
Browser