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Chapter 2: Problem 75

Explain how to solve the equation \(2 x+8=5 x-3\)

Short Answer

Expert verified
The solution to the equation \(2x + 8 = 5x - 3\) is \(x = \frac{11}{3}\).

Step by step solution

01

Group like terms

To begin with, we want all the \(x\) terms on one side of the equation and the numeric terms on the other. We can achieve this by subtracting \(2x\) from both sides of the equation and adding \(3\) to both sides of the equation. This will transform the equation as follows: \(2x - 2x + 8 + 3 = 5x - 2x - 3 + 3\), which simplifies to \(8 + 3 = 5x - 2x\).
02

Simplify the equation

Now, you can simplify both sides of the equation. On the left side, \(8 + 3\) simplifies to \(11\). On the right side, \(5x - 2x\) simplifies to \(3x\). So, the simplified equation becomes \(11 = 3x\).
03

Solve for the variable

Finally, to isolate the variable \(x\), we divide both sides of the equation by \(3\). This gives us the solution: \(x = \frac{11}{3}\).

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Most popular questions from this chapter

The bar graph shows average yearly earnings in the United States for people with a college education, by final degree earned. Exercises \(23-24\) are based on the data displayed by the graph. (GRAPH CANNOT COPY) The average yearly salary of an American whose final degree is a doctorate is 39 dollars thousand less than twice that of an American whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn 126 dollars thousand. Find the average yearly salary of Americans with each of these final degrees.

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