Problem 75 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \(8 + 3 = 5x - 2x\).

Step 2: 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 \(11 = 3x\).

Step 3: Solve for the variable

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