Solve for x: 2(4x - 9) = 14. Simplify your answer as much as possible.

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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

  1. 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:

$$ 8x - 18 = 14 $$

  1. 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:

$$ 8x = 32 $$

  1. 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.

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