Answer:
C) x² + 3 = 5x - 3 is not a linear equation
Explanation:
Linear equation:
In a linear equation, the highest power of variable is always 1.
Simplify each equation and check the highest power of each equation. If the highest power is 1, then it is a linear equation.
A) 2x + 3 = 7x - 2
Subtract 3 from both sides.
2x = 7x - 2 - 3
2x = 7x - 5
Subtract 7x from both sides.
2x -7x = -5
-5x = -5
Highest power is 1. This is a linear equation.
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B) x + 5 = 3x - 4
Subtract 5 from both sides.
x = 3x - 4 - 5
x = 3x - 9
Subtract 3x from both sides.
x - 3x = -9
-2x = - 9
Highest power is 1. This is a linear equation.
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c) x² +3 = 5x - 3
x² = 5x - 3 -3
x² = 5x - 6
x² - 5x = -6
Highest power is 2. This is NOT a linear equation.
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D) (x - 2)² = x² + 8
Expand (x - 2)² using the algebraic identity (a - b)² = a² - 2ab +b².
x² - 2*x*2 + 2² = x² + 8
x² - 4x + 4 = x² + 8
x² - 4x + 4 -x² = 8
-4x + 4 = 8
-4x = 8 - 4
-4x = 4
Highest power is 1. This is a linear equation.