91Ó°ÊÓ

When solving linear equations, the first step is to isolate the variable. This means getting the variable on its own on one side of the equation. In our exercise, the equation is: \(\frac{2h}{9}-3=15\). To isolate the variable term \( \frac{2h}{9} \), we need to get rid of the \( -3 \) on the left side.
We can do this by adding 3 to both sides of the equation. Here's how it looks: \[ \frac{2h}{9} - 3 + 3 = 15 + 3 \] The \( -3 \) and \( +3 \) cancel each other out, leaving us with: \[ \frac{2h}{9} = 18 \] Now we have the term \( \frac{2h}{9} \) isolated on one side of the equation, making it easier to solve for \( h \). Remember, isolating the variable is a crucial first step in solving any linear equation.

Once the variable term is isolated, the next step is to remove any fractions. Fractions can make equations harder to solve, so it's best to eliminate them early on. In our equation, \( \frac{2h}{9} = 18 \), we can remove the fraction by multiplying both sides of the equation by 9. Here’s how it works: \[ 9 \times \frac{2h}{9} = 18 \times 9 \] On the left side, \( 9 \) and \( \frac{2h}{9} \) cancel each other out, leaving us with: \[ 2h = 162 \] Now, the equation is simpler because we no longer have a fraction. Removing fractions helps to simplify the process of solving the equation.

After solving for the variable, it's essential to check your solution. This ensures that your solution is correct and satisfies the original equation. In our exercise, we found that \( h = 81 \). To check this, we substitute \( h = 81 \) back into the original equation: \[ \frac{2(81)}{9} - 3 = 15 \] First, calculate the multiplication and division: \[ \frac{162}{9} - 3 = 15 \] Simplify further: \[ 18 - 3 = 15 \] Since both sides of the equation are equal (15 = 15), the solution \( h = 81 \) is correct.
Always remember to check the solution to avoid any mistakes and ensure that the variable you found works in the original equation.