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Chapter 6: Problem 74

In Exercises 74-75, solve each proportion for \(x\). \(\frac{x+a}{a}=\frac{b+c}{c}\)

Short Answer

Expert verified
The solution for the variable \( x \) in the given proportion is \( x = a*\frac{b-c}{c} \).

Step by step solution

01

- Understanding the Proportion

In this given proportion, we can see four variables \( x, a, b, c \) with \( x \) being the variable we need to find, while \( a, b, c \) are constants. The equation, derived from the proportion, is \( \frac{x+a}{a}=\frac{b+c}{c} \).
02

- Cross-Multiply the Proportion

The first step to solve for \( x \) is to cross-multiply. Therefore, we have \( (x+a)*c = (b+c)*a \). This action will simplify the equation and eliminate denominators.
03

- Distribute Multiplication Over Addition

Now, distribute the multiplication over addition on both sides which will give \( c*x + c*a = b*a + a*c \).
04

- Re-arrange the variables

Look for like terms on both sides of the equation and re-arrange the equation accordingly: \( c*x - a*c = b*a - c*a \).
05

- Solving for x

Finally, divide both sides of the equation by \( c \) to isolate \( x \) in the equation, hence we will have \( x = \frac{b*a - c*a}{c} = a*\frac{b-c}{c} \).

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Most popular questions from this chapter

Explain how to solve a quadratic equation by factoring. Use the equation \(x^{2}+6 x+8=0\) in your explanation.

Solve: \(x^{2}+2 \sqrt{3} x-9=0\).

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Use FOIL to find the products in Exercises 1-8. \((x+3)(x+5)\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(-2 x+5 \geq 13\) and concluded that \(-4\) is the greatest integer in the solution set.
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