Questions: Solve the equation and check. 2(x-3)=31

Solution Steps

To solve the equation \(2(x-3)=31\), we first need to isolate the variable \(x\). We can do this by dividing both sides of the equation by 2, and then adding 3 to both sides. After finding the value of \(x\), we can substitute it back into the original equation to verify the solution.

We start with the equation: \[ 2(x - 3) = 31 \] To isolate \(x\), we first divide both sides by 2: \[ x - 3 = \frac{31}{2} \]

Next, we add 3 to both sides: \[ x = \frac{31}{2} + 3 \] To express 3 as a fraction, we write it as \(\frac{6}{2}\): \[ x = \frac{31}{2} + \frac{6}{2} = \frac{37}{2} \]

Now, we check our solution by substituting \(x = \frac{37}{2}\) back into the original equation: \[ 2\left(\frac{37}{2} - 3\right) = 2\left(\frac{37}{2} - \frac{6}{2}\right) = 2\left(\frac{31}{2}\right) = 31 \] Since both sides of the equation are equal, our solution is verified.

Final Answer