answer :
8
steps:
NO SOLUTION means something like where the equation is
0 = 12
where number on the left of the equal sign is different from the number on the right of the equal sign
Okay, let's solve this step-by-step:
2(4x - 5) = ax + 2
Distribute the 2 on the left side:
8x - 10 = ax + 2
Group the x terms together:
8x - ax = 10 + 2
Combine like terms:
8x - ax = 12
Add ax to both sides:
8x = ax + 12
Subtract ax from both sides:
8x - ax = 12
Factor out x:
x(8 - a) = 12
For the equation to have no solution, x(8 - a) cannot equal 12 for any value of x. This happens when 8 - a = 0.
So a = 8 is the value that makes the original equation have no solution.
0 = 12
The key is that when a = 8, it causes both sides of the final factored equation to equal 0 for all values of x, meaning there are NO values of x that can satisfy the equation.
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