Question

Find out the errors and correct them for each question(Make LHS=RHS)

a.(2x)²=2x².
b.x(2x+3)=(2x²+3).
c.(2x-3y)²=4x²-9y².
d.2x+3/2=x+3

Answer 1

a. The equation (2x)² = 2x² is incorrect. b. The equation x(2x+3) = (2x²+3) is incorrect. c. The equation (2x-3y)² = 4x²-9y² is incorrect. d. The equation 2x + 3/2 = x + 3 is correct when x = 3/2.

Step-by-step explanation:

1. a. (2x)² = 2x²: The left-hand side (LHS) of the equation is (2x)², which means (2x) multiplied by itself. Simplifying this, we get 4x². The right-hand side (RHS) of the equation is 2x². Since 4x² is not equal to 2x², the given equation is incorrect.
   
   
2. b. x(2x+3) = (2x²+3): The LHS of the equation is x multiplied by (2x+3). Expanding this expression, we get 2x² + 3x. The RHS of the equation is 2x² + 3. Since 2x² + 3x is not equal to 2x² + 3, the given equation is incorrect.
   
   
3. c. (2x-3y)² = 4x²-9y²: The LHS of the equation is (2x-3y)², which means (2x-3y) multiplied by itself. Expanding this expression, we get 4x² - 12xy + 9y². The RHS of the equation is 4x² - 9y². Since 4x² - 12xy + 9y² is not equal to 4x² - 9y², the given equation is incorrect.
   
   
4. d. 2x + 3/2 = x + 3: The LHS of the equation is 2x + 3/2. To make the equation easier to solve, we can multiply the entire equation by 2 to remove the fraction. This gives us 4x + 3 = 2x + 6. Simplifying this, we get 2x = 3. Solving for x, we find that x = 3/2. So, the equation is correct when x = 3/2.