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The equations have become wrong because ...

The equations have become wrong because of the wrong order of signs. Choose the correct order of signs from the four options given below so as to make the equations right. Write the alternative number of the correct option on the answer sheet against the corresponding question number-
`12- 4 + 2 + 3 =9`

A

`+ + = -`

B

`+ = + -`

C

`= div - +`

D

`div xx + =`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \( 12 - 4 + 2 + 3 = 9 \) and find the correct order of operations, we will evaluate the options provided. ### Step-by-Step Solution: 1. **Evaluate the Original Equation**: \[ 12 - 4 + 2 + 3 \] Calculate \( 12 - 4 \): \[ 12 - 4 = 8 \] Now, add \( 2 \): \[ 8 + 2 = 10 \] Finally, add \( 3 \): \[ 10 + 3 = 13 \] Thus, the left-hand side equals \( 13 \), which does not equal \( 9 \). 2. **Check the First Option**: If we change the signs to \( +, +, =, - \): \[ 12 + 4 + 2 = 3 - 9 \] Calculate \( 12 + 4 + 2 \): \[ 12 + 4 = 16 \] \[ 16 + 2 = 18 \] The right-hand side becomes \( 3 - 9 = -6 \). Thus, \( 18 \neq -6 \). 3. **Check the Second Option**: If we change the signs to \( +, =, +, - \): \[ 12 + 4 = 2 + 3 - 9 \] Calculate \( 12 + 4 \): \[ 12 + 4 = 16 \] Calculate the right-hand side: \[ 2 + 3 - 9 = 5 - 9 = -4 \] Thus, \( 16 \neq -4 \). 4. **Check the Third Option**: If we change the signs to \( =, /, -, + \): \[ 12 = 4 / 2 - 3 + 9 \] Calculate \( 4 / 2 \): \[ 4 / 2 = 2 \] Now, calculate the right-hand side: \[ 2 - 3 + 9 = -1 + 9 = 8 \] Thus, \( 12 \neq 8 \). 5. **Check the Fourth Option**: If we change the signs to \( /, *, +, = \): \[ 12 / 4 * 2 + 3 = 9 \] Calculate \( 12 / 4 \): \[ 12 / 4 = 3 \] Now, multiply by \( 2 \): \[ 3 * 2 = 6 \] Finally, add \( 3 \): \[ 6 + 3 = 9 \] Thus, \( 9 = 9 \) is true. ### Conclusion: The correct order of signs is given in the **fourth option**.
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