We are given the linear equation 4x minus 5 equals 17. Our goal is to find the value of x that makes this equation true.
Think of an equation as a balanced scale. The left side, 4x minus 5, must equal the right side, 17. Whatever we do to one side, we must do to the other to keep the scale balanced.
To isolate the term with x, we'll add 5 to both sides of the equation. This eliminates the minus 5 on the left side. The equation becomes: 4x minus 5 plus 5 equals 17 plus 5. Simplifying both sides gives us: 4x equals 22.
Now we need to isolate x by dividing both sides by 4. This cancels out the coefficient of x on the left side. The equation becomes: 4x divided by 4 equals 22 divided by 4. Simplifying gives us: x equals 5.5.
To verify our solution, we substitute x equals 5.5 back into the original equation. This gives us: 4 times 5.5 minus 5 equals 17. Calculating the left side: 22 minus 5 equals 17. Since both sides equal 17, our solution is correct.
Let's summarize our solution process. We started with the equation 4x minus 5 equals 17. First, we added 5 to both sides to get 4x equals 22. Then, we divided both sides by 4 to find x equals 5.5. Finally, we verified our solution by substituting back into the original equation, confirming that both sides equal 17.