We are given the linear equation 2x plus 3 equals 8x minus 9. Our goal is to find the value of x that makes both sides of this equation equal. This is a linear equation in one variable, and we'll solve it by isolating x on one side.
To solve this equation, we first collect like terms. We'll subtract 2x from both sides to move all x terms to one side. On the left side, 2x minus 2x cancels out, leaving us with 3. On the right side, 8x minus 2x gives us 6x, so we have 6x minus 9. Now our equation is 3 equals 6x minus 9.
Now we need to isolate the variable term. We'll add 9 to both sides to move the constant term to the left. On the left side, 3 plus 9 equals 12. On the right side, negative 9 plus 9 cancels out, leaving us with just 6x. Our equation is now 12 equals 6x.
To find the value of x, we divide both sides by 6. On the left side, 12 divided by 6 equals 2. On the right side, 6x divided by 6 simplifies to just x. This gives us 2 equals x, which is the same as x equals 2. So our solution is x equals 2.
To verify our solution, we substitute x equals 2 back into the original equation. For the left side, we have 2 times 2 plus 3, which is 4 plus 3, equaling 7. For the right side, we have 8 times 2 minus 9, which is 16 minus 9, also equaling 7. Since both sides equal 7, our solution x equals 2 is correct.
Let's summarize the steps to solve this equation. First, we started with the original equation: 2x plus 3 equals 8x minus 9. Second, we subtracted 2x from both sides to get 3 equals 6x minus 9. Third, we added 9 to both sides to get 12 equals 6x. Fourth, we divided both sides by 6 to find that x equals 2. Finally, we verified our solution by substituting x equals 2 back into the original equation and confirming that both sides equal 7. Therefore, x equals 2 is the correct solution.