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Chapter 6: Problem 50

Solve and check each equation. \(\frac{z}{5}-\frac{1}{2}=\frac{z}{6}\)

Short Answer

Expert verified
The solution to the equation is \(z = 15\).

Step by step solution

01

Clear the Fractions

Multiply every term in the equation by 30 to eliminate the fractions. This will result in the equation: \(6z-15=5z\).
02

Simplify and Solve

Subtract \(5z\) from both sides to isolate \(z\). This results in \(z=15\).
03

Check the Solution

Substitute the obtained value for \(z\) back into the original equation to verify the solution. Substituting \(z = 15\) yields \(\frac{15}{5}-\frac{1}{2}=\frac{15}{6}\), which simplifies to \(3-0.5=2.5\). Since the left side equals the right side, the solution \(z = 15\) is correct.

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Most popular questions from this chapter

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(8 x^{2}+33 x+4\)

Use FOIL to find the products. \((x-5)(x+3)\)

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. It's easy to factor \(x^{2}+x+1\) because of the relatively small numbers for the constant term and the coefficient of \(x\).
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