Solve for x: 2(4x - 9) = 14. Simplify your answer as much as possible.
Understand the Problem
The question is asking us to solve the equation 2(4x - 9) = 14 for the variable x and to simplify the answer as much as possible.
Answer
The value of $x$ is $4$.
Answer for screen readers
The solution for $x$ is $4$.
Steps to Solve
- Distribute the 2 inside the parentheses
To eliminate the parentheses, multiply 2 by each term inside the parentheses:
$$ 2(4x - 9) = 2 \cdot 4x - 2 \cdot 9 = 8x - 18 $$
Now, the equation becomes:
$$ 8x - 18 = 14 $$
- Add 18 to both sides
To isolate the term with $x$, add 18 to both sides of the equation:
$$ 8x - 18 + 18 = 14 + 18 $$
This simplifies to:
$$ 8x = 32 $$
- Divide both sides by 8
To solve for $x$, divide both sides of the equation by 8:
$$ x = \frac{32}{8} $$
This simplifies to:
$$ x = 4 $$
The solution for $x$ is $4$.
More Information
This equation involves distributing a term across parentheses and isolating the variable. Knowing how to manipulate equations step-by-step is crucial in algebra.
Tips
- Forgetting to distribute correctly, which can lead to incorrect coefficients.
- Not combining like terms properly after simplification.
To avoid these mistakes, carefully read each step and verify your calculations before moving to the next step.
