Solve for x in the equation x/18 = 2/3.

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Understand the Problem

The question is asking us to solve for the variable x in the equation x/18 = 2/3. This requires isolating x by manipulating the equation.

Answer

The solution is $x = 12$.
Answer for screen readers

The solution is $x = 12$.

Steps to Solve

  1. Cross-Multiply to Eliminate the Fraction To solve the equation $\frac{x}{18} = \frac{2}{3}$, we can cross-multiply: $$ x \cdot 3 = 2 \cdot 18 $$

  2. Calculate the Right Side Now calculate $2 \cdot 18$: $$ 2 \cdot 18 = 36 $$ So the equation now is: $$ 3x = 36 $$

  3. Isolate x by Dividing To find $x$, divide both sides by 3: $$ x = \frac{36}{3} $$

  4. Calculate the Final Value Now perform the division: $$ x = 12 $$

The solution is $x = 12$.

More Information

This problem demonstrates the use of cross-multiplication to solve proportions, a common technique in algebra. Understanding how to manipulate equations is essential for solving many types of equations.

Tips

  • Mistake: Forgetting to cross-multiply correctly. How to Avoid: Always ensure both sides of the equation are multiplied properly; double-check your setup.

  • Mistake: Incorrectly dividing or multiplying after cross-multiplying. How to Avoid: Carefully perform arithmetic operations and verify each computation step.

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