Question

solve the equation 6.3g + 10 = 2.3g + 26. 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: Isolate variable terms

Subtract $2.3g$ from both sides:
$6.3g - 2.3g+10 = 2.3g - 2.3g+26$
$4g + 10=26$

Step2: Isolate the term with the variable

Subtract 10 from both sides:
$4g+10 - 10=26 - 10$
$4g = 16$

Step3: Solve for g

Divide both sides by 4:
$\frac{4g}{4}=\frac{16}{4}$
$g = 4$

Step4: Checking the solution (for part b)

To check if $g = 4$ is correct, substitute $g = 4$ into the original equation.
Left - hand side: $6.3\times4+10=25.2 + 10=35.2$
Right - hand side: $2.3\times4+26=9.2+26 = 35.2$
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 the result is incorrect because when a value is a solution of an equation, substituting it into the equation should make the equation a true statement.

Answer:

a. $g = 4$
b. To check, substitute $g = 4$ into the original equation. If the left - hand side equals the right - hand side, the solution is correct. If not, the result is incorrect because a solution makes the equation a true statement.