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Chapter 6: Problem 47

Solve and check each equation. \(\frac{x}{3}+\frac{x}{2}=\frac{5}{6}\)

Short Answer

Expert verified
The solution to the equation is \(x=1\).

Step by step solution

01

Find common denominator

To clear the fractions, find a common denominator for \(3\), \(2\), and \(6\). The least common multiple of \(3\), \(2\), and \(6\) is \(6\). Therefore multiply each term of the equation by \(6\). This leads to the new equation: \(2x+3x=5\).
02

Simplify the expression

Combine like terms on the left side of the equation to simplify it further: \(5x=5\).
03

Solve for \(x\)

Now solve for \(x\) by dividing both sides of the equation by 5. This simplifies to \(x=1\).
04

Check the Solution

Substitute \(x=1\) back into the original equation and check if the left side equals the right side. Plugging in gives \(\frac{1}{3} + \frac{1}{2} = \frac{5}{6}\), which indeed is a true statement.

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