Solve the equation: 14x - 9 + 2x - 5 = 13x - 3 + 2x.
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
- Combine like terms on the left side
For the left side of the equation, combine the $x$ terms and the constant terms:
$$ 14x + 2x - 9 - 5 = 16x - 14 $$
- Combine like terms on the right side
For the right side of the equation, combine the $x$ terms and the constant terms:
$$ 13x + 2x - 3 = 15x - 3 $$
- Set the combined equations equal to each other
Now we have the simplified equation:
$$ 16x - 14 = 15x - 3 $$
- Isolate the variable
Subtract $15x$ from both sides to isolate $x$:
$$ 16x - 15x - 14 = -3 $$
This simplifies to:
$$ x - 14 = -3 $$
- 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.
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