Question

part 1 of 2 solve the equation 5 + 5g + 5 = 1 + 4g + 13. 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. (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Combine like - terms

Combine the terms with \(g\) on the left - hand side of the equation \(5g + 5=14g+13\). Subtract \(5g\) from both sides:
\[5g + 5-5g=14g + 13-5g\]
\[5 = 9g+13\]

Step2: Isolate the term with \(g\)

Subtract 13 from both sides of the equation:
\[5-13=9g+13 - 13\]
\[-8 = 9g\]

Step3: Solve for \(g\)

Divide both sides by 9:
\[g=\frac{-8}{9}\approx - 0.89\]

To check if the value of \(g\) is correct, substitute \(g =-\frac{8}{9}\) into the original equation:
Left - hand side: \(5\times(-\frac{8}{9})+5=-\frac{40}{9}+5=-\frac{40}{9}+\frac{45}{9}=\frac{-40 + 45}{9}=\frac{5}{9}\)
Right - hand side: \(14\times(-\frac{8}{9})+13=-\frac{112}{9}+13=-\frac{112}{9}+\frac{117}{9}=\frac{-112 + 117}{9}=\frac{5}{9}\)

Since the left - hand side equals the right - hand side when \(g =-\frac{8}{9}\), the solution is correct.

Answer:

\(g=-\frac{8}{9}\)