Question

solve the equation 4.1g + 10 = 2.1g + 16.
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 = 3
(simplify your answer. type an integer or a decimal.)
b. choose the correct explanation below.
o a. substitute the value for g on one side of the equation to check the answer. if the check does not work, then the answer must be incorrect.
o b. substitute the value for g on one side of the equation to check the answer. if the check does not work, either the answer is incorrect or there were errors made when checking.
o c. substitute the value for g on both sides of the equation to check the answer. if the check does not work, either the answer is incorrect or there were errors made when checking.
o d. substitute the value for g on both sides of the equation to check the answer. if the check does not work, then the answer must be incorrect.

Explanation:

Step1: Solve the equation

Given \(4.1g + 10=2.1g + 16\).
Subtract \(2.1g\) from both sides:
\(4.1g-2.1g + 10=2.1g-2.1g + 16\)
\(2g+10 = 16\).
Subtract \(10\) from both sides:
\(2g+10 - 10=16 - 10\)
\(2g=6\).
Divide both sides by \(2\):
\(g=\frac{6}{2}=3\).

Step2: Check the solution

To check if \(g = 3\) is correct, substitute \(g = 3\) into the original equation.
Left - hand side (LHS): \(4.1\times3+10=12.3 + 10=22.3\).
Right - hand side (RHS): \(2.1\times3+16=6.3+16=22.3\).
Since \(LHS = RHS\), the solution \(g = 3\) is correct.

Answer:

a. \(g = 3\)
b. Substitute the value for \(g\) on both sides of the equation to check the answer. If the check does not work, then the answer must be incorrect. In this case, when \(g = 3\), \(4.1\times3+10=2.1\times3 + 16\) (both equal to \(22.3\)), so the value of \(g = 3\) is correct.