Question

a. find the value of g. 6.9g + 8 = 3.9g + 20
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 to one side

Subtract $3.9g$ from both sides of the equation $6.9g + 8=3.9g + 20$.
$6.9g-3.9g + 8=3.9g-3.9g + 20$, which simplifies to $3g+8 = 20$.

Step2: Isolate the term with the variable

Subtract 8 from both sides of the equation $3g+8 = 20$.
$3g+8 - 8=20 - 8$, which gives $3g=12$.

Step3: Solve for g

Divide both sides of the equation $3g = 12$ by 3.
$\frac{3g}{3}=\frac{12}{3}$, so $g = 4$.

To check:
Substitute $g = 4$ into the original equation $6.9g+8=3.9g + 20$.
Left - hand side: $6.9\times4+8=27.6 + 8=35.6$.
Right - hand side: $3.9\times4+20=15.6+20 = 35.6$.
Since the left - hand side equals the right - hand side when $g = 4$, the solution is correct. If the check does not work, it means there was an error in the solving process, because for a linear equation, a value of the variable that satisfies the original equation is the correct solution.

Answer:

a. $g = 4$
b. To check, substitute $g = 4$ into the original equation. Calculate the left - hand side ($6.9\times4+8$) and the right - hand side ($3.9\times4 + 20$). If they are equal, the value of $g$ is correct. If the check does not work, it likely means there was an error in the solving process, as a correct solution should make the original equation true.