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

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

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 (for part b)

Substitute \(g = 2\) into the original equation.
Left - hand side (LHS): \(5.3\times2+9=10.6 + 9=19.6\)
Right - hand side (RHS): \(2.3\times2+15=4.6+15 = 19.6\)
Since \(LHS = RHS\), \(g = 2\) is the correct solution. If the check does not work, it means there was an error in the solving process. Because when we substitute the value of the variable into the original equation, if the two sides of the equation are not equal, then the value of the variable does not satisfy the equation.

Answer:

a. \(g = 2\)
b. Substitute \(g = 2\) into the original equation \(5.3g + 9\) and \(2.3g + 15\). Calculate \(5.3\times2+9=19.6\) and \(2.3\times2 + 15=19.6\). Since they are equal, \(g = 2\) is correct. If the check fails, the result is incorrect because the solution must satisfy the original equation.