If 3x – 13 = 8, the value of x – 1 is
The correct answer and explanation is:
We are given the equation: 3x−13=83x – 13 = 8
Step 1: Solve for xx
To isolate xx, we first get rid of the constant on the left-hand side: 3x−13+13=8+133x=213x – 13 + 13 = 8 + 13 \\ 3x = 21
Now divide both sides by 3: x=213=7x = \frac{21}{3} = 7
Step 2: Find the value of x−1x – 1
Now that we know x=7x = 7, substitute that into x−1x – 1: x−1=7−1=6x – 1 = 7 – 1 = \boxed{6}
300-Word Explanation:
This problem is a basic linear equation, which is a fundamental concept in algebra. The equation given is 3x−13=83x – 13 = 8. The goal is to isolate the variable xx on one side of the equation in order to find its value. This process involves two main steps: removing constants and then removing coefficients.
First, we add 13 to both sides of the equation to eliminate the “-13” on the left-hand side. Adding the same value to both sides of an equation is allowed because it maintains equality — it’s like balancing a scale. When we do this, we get: 3x=213x = 21
Next, we want to solve for xx, but it’s currently multiplied by 3. To undo this multiplication, we divide both sides by 3: x=7x = 7
This gives us the value of xx. But the question doesn’t ask directly for xx; it asks for x−1x – 1. This is a simple substitution step. Since x=7x = 7, we compute 7−17 – 1, which equals 6.
This problem illustrates how solving equations can be methodical and logical. Each operation you perform has a clear purpose, and it brings you closer to isolating the variable. These steps — adding, subtracting, multiplying, and dividing — are the basic tools used throughout algebra to solve equations. Understanding them builds a strong foundation for more advanced math.
Final Answer:
6\boxed{6}