1. Solve the equation 4(X-5)=8 for x. Which of the following is the correct answer?
Answer: A
x = 7
To solve the equation 4(X-5)=8 for x, we first divide both sides by 4, yielding X-5=2. Adding 5 to both sides results in X=7.
A) 7
This option is correct because substituting x = 7 back into the original equation gives 4(7-5) = 4(2) = 8, which is true and verifies the solution.
B) 3/4
This option is incorrect. If we substitute x = 3/4 into the equation, we would get 4(3/4-5) = 4(-19/4) = -19, which does not equal 8.
C) 3 1/4
This option is also incorrect. Substituting x = 3 1/4 (or 13/4) into the equation results in 4(13/4 - 5) = 4(-7/4) = -7, which does not satisfy the equation.
D) -3
This option is incorrect as well. Substituting x = -3 gives 4(-3-5) = 4(-8) = -32, which is not equal to 8.
Conclusion
The correct answer is x = 7, as it satisfies the original equation perfectly. All other options either lead to incorrect results or do not fulfill the equation's requirements, confirming that they are not valid solutions.