Question

solve the equation. Show how to check your solution. $$\frac{1}{2} x-9=11$$

Short answer

The solution to the equation is \(x = 40\). This was verified by check, substituting the solution back into the original equation.

Step-by-step solution

Isolate the term with the variable

The first step is to isolate the term that has the variable \(x\). You can do this by adding 9 to both sides of the equation. This will result in the equation \(\frac{1}{2} x = 20\).

Solve for the variable

You now need to completely isolate \(x\). This is done by multiplying both sides of the equation by the reciprocal of the coefficient of \(x\). In this situation, the coefficient of \(x\) is \(\frac{1}{2}\), so you will multiply both sides by 2. This will give you \(x = 40\).

Check the solution

You can check the correctness of the solution by substituting \(x = 40\) into the original equation and seeing if both sides satisfy the equality. This would be performed as follows: left side = \(\frac{1}{2} \cdot 40 - 9 = 11\); right side = 11. As both sides are equal, the solution \(x = 40\) can be confirmed as correct.