Final answer:
To find the value of 'a' in the equation 4x - 2(x + a) = 8 when x = 7, we substitute and simplify to get 14 - 2a = 8, which gives us a = 3 after solving.
Step-by-step explanation:
The question asks for the value of 'a' that makes the equation 4x - 2(x + a) = 8 true when x = 7. To find the value of 'a', we substitute x with 7 in the equation and simplify.
Step 1: Substitute x with 7.
4(7) - 2(7 + a) = 8
Step 2: Simplify the equation.
28 - 14 - 2a = 8
Step 3: Combine like terms.
14 - 2a = 8
Step 4: Isolate the variable 'a'.
14 - 8 = 2a
6 = 2a
Step 5: Solve for 'a'.
a = 6/2
a = 3
Therefore, the value of 'a' is 3.
Step 6: Eliminate and simplify wherever possible to verify the solution.
Step 7: Check if the answer is reasonable by substituting 'a' back into the original equation.
4(7) - 2(7 + 3) = 8 simplifies to 28 - 2(10) = 8, which is true as 28 - 20 = 8.