Solve for x in the equation x/18 = 2/3.
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
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Cross-Multiply to Eliminate the Fraction To solve the equation $\frac{x}{18} = \frac{2}{3}$, we can cross-multiply: $$ x \cdot 3 = 2 \cdot 18 $$
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Calculate the Right Side Now calculate $2 \cdot 18$: $$ 2 \cdot 18 = 36 $$ So the equation now is: $$ 3x = 36 $$
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Isolate x by Dividing To find $x$, divide both sides by 3: $$ x = \frac{36}{3} $$
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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
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Mistake: Forgetting to cross-multiply correctly. How to Avoid: Always ensure both sides of the equation are multiplied properly; double-check your setup.
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Mistake: Incorrectly dividing or multiplying after cross-multiplying. How to Avoid: Carefully perform arithmetic operations and verify each computation step.
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