Final answer:
Solve for w from the equation -2w - 3 = 3 to get w = -3. Then, substitute w into 5w + 2 to find the value, resulting in -13 after simplification.
Step-by-step explanation:
First, we will solve the equation -2w - 3 = 3 for the variable w. To find w, we add 3 to both sides of the equation, which gives us -2w = 6. Then, we divide both sides by -2 to isolate w which results in w = -3. Now that we have the value of w, we can substitute it into the original expression 5w + 2. Substituting w with -3 gives us 5(-3) + 2, which simplifies to -15 + 2. Adding these together results in -13, which is the simplified value of the expression.
Remember to check the answer to see if it seems reasonable. In this case, substituting the value of w back into the original equation -2w - 3 = 3 confirms the correctness as -2(-3) - 3 = 6 - 3 = 3, which is indeed the given value.