We are given the linear equation 3x minus 5 equals 15. Our goal is to find the value of x that makes this equation true. Let's break down the components: 3 is the coefficient of x, minus 5 is a constant term on the left side, and 15 is the constant term on the right side.
To solve for x, we use the principle of isolating the variable. This means we need to get x by itself on one side of the equation. We can think of an equation like a balance scale - both sides must remain equal. Whatever operation we perform on one side, we must also perform on the other side to maintain balance. Our strategy is to undo the operations applied to x in reverse order.
Our first step is to eliminate the minus five on the left side. To do this, we add five to both sides of the equation. On the left side, we have 3x minus 5 plus 5. The minus 5 and plus 5 cancel each other out, leaving us with just 3x. On the right side, we have 15 plus 5, which equals 20. So our equation simplifies to 3x equals 20.
Now we need to eliminate the coefficient 3 that is multiplied by x. To do this, we divide both sides of the equation by 3. On the left side, we have 3x divided by 3. The 3s cancel out, leaving us with just x. On the right side, we have 20 divided by 3, which gives us the fraction 20 thirds. So our final equation is x equals 20 thirds.
To verify our solution, we substitute x equals 20 thirds back into the original equation. We replace x with 20 thirds in 3x minus 5 equals 15. This gives us 3 times 20 thirds minus 5 equals 15. When we multiply 3 by 20 thirds, the 3s cancel out, leaving us with 20. So we have 20 minus 5 equals 15. Simplifying the left side, we get 15 equals 15. Since both sides are equal, our solution is correct.
Let's summarize the complete solution process. First, we started with the original equation: 3x minus 5 equals 15. Second, we added 5 to both sides to isolate the term with x, resulting in 3x equals 20. Third, we divided both sides by 3 to solve for x, giving us x equals 20 thirds. Finally, we can express this answer in different forms: as an improper fraction 20 thirds, as a mixed number 6 and 2 thirds, or as a decimal approximation 6.67. The solution to the equation 3x minus 5 equals 15 is x equals 20 thirds.