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Chapter 6: Problem 87

Solve each equation. Use set notation to express solution sets for equations with no solution or equations that are true for all real numbers. \(\frac{x}{3}=\frac{x}{2}\)

Short Answer

Expert verified
The solution to the equation is \{0\}

Step by step solution

01

Multiply both sides by 6

By multiplying both sides by 6, you can eliminate the denominators 3 and 2 for a simpler equation. This gives you \(2x=3x\).
02

Subtract 2x from both sides

To isolate x, subtract 2x from both sides of the equation. Doing so gives the equation \(0=x\). It means x must be zero for the equation to hold true.
03

Confirm solution

Now, put this value back into the initial equation. \(x=0\) in the initial equation gives \(\frac{0}{3}=\frac{0}{2}\), which is a true statement. Thus, the solution is confirmed. x must be zero.
04

Express the solution set

The solution set, in this case, consists of only one number: zero. In set notation, this is written as \{0\}. This indicates that the set includes only the number zero.

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Most popular questions from this chapter

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(x^{2}-7 x-44\)

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When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.
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