Question

1. solve the equation 5.3g + 9 = 2.3g + 15.

a. find the value of g.
b. explain how you can check that the value you found for g is correct. if your check does not work, does that mean that your result is incorrect? explain.

Explanation:

Step1: Subtract \(2.3g\) from both sides

$$\begin{align*} 5.3g + 9-2.3g&=2.3g + 15-2.3g\\ 3g+9&=15 \end{align*}$$

Step2: Subtract \(9\) from both sides

$$\begin{align*} 3g+9 - 9&=15-9\\ 3g&=6 \end{align*}$$

Step3: Divide both sides by \(3\)

$$\begin{align*} \frac{3g}{3}&=\frac{6}{3}\\ g&=2 \end{align*}$$

Step4: Check the solution

Substitute \(g = 2\) into the original equation:
Left - hand side: \(5.3\times2+9=10.6 + 9=19.6\)
Right - hand side: \(2.3\times2+15=4.6+15 = 19.6\)
Since the left - hand side equals the right - hand side when \(g = 2\), the solution is correct. If the check does not work, it means there was an error in the solving process.

Answer:

a. \(g = 2\)
b. Substitute the value of \(g\) into the original equation. Calculate the left - hand side and the right - hand side. If they are equal, the value is correct. If not, there is an error in solving. If the check fails, the result is incorrect because the check is a verification of the solution in the original equation.