Question

m/j grade 8 pre - alg - trujillo (lms) 3 - 2: mathxl for school: practice & problem solving (lms graded) due oct 3 - 11:59 pm late part 1 of 2 solve the equation 3.2g + 6 = 1.2g + 10. 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. a. g = (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Move like - terms together

Subtract \(1.2g\) from both sides and subtract 6 from both sides of the equation \(3.2g + 6=1.2g + 10\). We get \(3.2g-1.2g=10 - 6\).

Step2: Simplify both sides

On the left - hand side, \(3.2g-1.2g=(3.2 - 1.2)g = 2g\). On the right - hand side, \(10 - 6 = 4\). So the equation becomes \(2g=4\).

Step3: Solve for \(g\)

Divide both sides of the equation \(2g = 4\) by 2. We have \(g=\frac{4}{2}=2\).

To check if \(g = 2\) is correct, substitute \(g = 2\) into the original equation:
Left - hand side: \(3.2\times2+6=6.4 + 6=12.4\).
Right - hand side: \(1.2\times2+10=2.4 + 10=12.4\). Since the left - hand side equals the right - hand side when \(g = 2\), the value of \(g\) is correct. If the check does not work, it does not necessarily mean the result is incorrect. It could be due to an error in the checking process (such as a calculation mistake while substituting and computing).

Answer:

a. \(g = 2\)
b. Substitute \(g = 2\) into the original equation. Calculate the left - hand side \(3.2\times2+6=12.4\) and the right - hand side \(1.2\times2 + 10=12.4\). Since they are equal, \(g = 2\) is correct. If the check does not work, it may be due to a calculation error in the check, not necessarily an incorrect result for \(g\).