8 ( 4 x − 5 ) − 12 = 20 x − 10
32 x − 40 − 12 = 20 x − 10
32 x − 52 = 20 x − 10
32 x − 52 − 20 x = − 10
12 x − 52 = − 10
12 x = − 10 + 52
12 x = 42
x = 12 42
x = 2 7
x = 3 2 1 ≈ 3.5
8 ( 4 x − 5 ) − 12 = 20 x − 10 32 x − 40 − 12 = 20 x − 10 12 x = 42 x = 12 42 = 2 7
To solve ( 2 x ) 2 = 4.0 ( 1 − x ) 2 , take the square root of both sides, simplify the equations, and find that the only solution is x = 2 1 . The second case results in a contradiction, confirming our original solution. Therefore, x = 2 1 is the sole solution.
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