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 = (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Simplify the equation

$$\begin{align*} 4.1g + 10&=2.1g+16\\ 4.1g-2.1g&=16 - 10\\ 2g&=6 \end{align*}$$

Step2: Solve for \(g\)

Divide both sides of the equation \(2g = 6\) by \(2\):
$$g=\frac{6}{2}=3$$

Step3: Check the solution

Substitute \(g = 3\) into the original equation:
Left - hand side: \(4.1\times3+10=12.3 + 10=22.3\)
Right - hand side: \(2.1\times3+16=6.3+16=22.3\)

Since the left - hand side equals the right - hand side when \(g = 3\), the solution is correct.

Answer:

a. \(g = 3\)
b. To check if the value of \(g\) is correct, substitute \(g\) into the original equation. Calculate the left - hand side (\(LHS\)) and the right - hand side (\(RHS\)) of the equation \(4.1g + 10=2.1g+16\). If \(LHS = RHS\), then the value of \(g\) is correct. In this case, when \(g = 3\), \(LHS=4.1\times3 + 10=12.3+10 = 22.3\) and \(RHS=2.1\times3+16=6.3 + 16=22.3\). So \(g = 3\) is the correct solution. If the check does not work, it may mean there was an error in the algebraic manipulation (such as a mistake in combining like terms or in the division/multiplication steps while solving for the variable). But in our case, the check works.