### Find and correct the errors in the following mathematical statements:

### Question 1. 4(x – 5) = 4x – 5

**Solution:**

Given: 4(x – 5) = 4x – 5

Now we check if the given statement is correct or not

Taking L.H.S:

= 4(x – 5)

= 4x – 20

L.H.S ≠ R.H.S

So, the correct solution of 4(x – 5) = 4x – 20

### Question 2. x(3x + 2) = 3x^{2}+ 2

**Solution:**

Given: x(3x + 2) = 3x

^{2}+ 2Now we check if the given statement is correct or not

Taking L.H.S:

= x(3x + 2)

= 3x

^{2 }+ 2xL.H.S ≠ R.H.S

So, the correct solution of x(3x + 2) = 3x

^{2}+ 2x

### Question 3. 2x + 3y = 5xy

**Solution:**

Given: 2x + 3y = 5xy

Here, L.H.S ≠ R.H.S

So, the correct solution of 2x + 3y = 2x + 3y

### Question 4. x + 2x + 3x = 5x

**Solution:**

Given: x + 2x + 3x = 5x

Now we check if the given statement is correct or not

Taking L.H.S:

= x + 2x + 3x

= 6x

L.H.S ≠ R.H.S

So, the correct solution of x + 2x + 3x = 6x

### Question 5. 5y + 2y + y – 7y = 0

**Solution:**

Given: 5y + 2y + y – 7y = 0

Now we check if the given statement is correct or not

Taking L.H.S:

= 5y + 2y + y – 7y

= y

L.H.S ≠ R.H.S

So, the correct solution of 5y + 2y + y – 7y = y

### Question 6. 3x + 2x = 5x^{2}

**Solution:**

Given: 3x + 2x = 5x

^{2}Now we check if the given statement is correct or not

Taking L.H.S:

= 3x + 2x

= 5x

L.H.S ≠ R.H.S

So, the correct solution of 3x + 2x = 5x

### Question 7. (2x)^{2}+ 4(2x) + 7 = 2x^{2}+ 8x + 7

**Solution:**

Given: (2x)

^{2}+ 4(2x) + 7 = 2x^{2}+ 8x + 7Now we check if the given statement is correct or not

Taking L.H.S:

= (2x)

^{2}+ 4(2x) + 7= 4x

^{2}+ 8x + 7L.H.S ≠ R.H.S

So, the correct solution of (2x)

^{2}+ 4(2x) + 7 = 4x^{2}+ 8x + 7

### Question 8. (2x)^{2}+ 5x = 4x + 5x = 9x

**Solution:**

Given: (2x)

^{2}+ 5x = 4x + 5x = 9xHere,

4x + 5x ≠ 9x

So, we check (2x)

^{2}+ 5x = 4x + 5x or notTaking L.H.S:

= (2x)

^{2}+ 5x= 4x

^{2}+ 5xL.H.S ≠ R.H.S

So, the correct solution of (2x)

^{2}+ 5x = 4x^{2}+ 5x

### Question 9. (3x + 2)^{2}= 3x^{2}+ 6x + 4

**Solution:**

Given: (3x + 2)

^{2}= 3x^{2}+ 6x + 4Now we check if the given statement is correct or not

Taking L.H.S:

= (3x + 2)

^{2}= 9x

^{2}+ 6x + 4L.H.S ≠ R.H.S

So, the correct solution of (3x + 2)

^{2 }= 9x^{2}+ 6x + 4

### Question 10. Substituting x = – 3 in

### (a) x^{2}+ 5x + 4 gives (– 3)^{2} + 5 (-3) + 4 = 9 + 2 + 4 = 15

**Solution:**

Given: x

^{2}+ 5x + 4Now substitute the value of x = -3 in the given equation,

= (-3)

^{2}+ 5(-3) + 4= 9 – 15 + 4

= -2

So the correct solution of x

^{2}+ 5x + 4 = -2

### (b) x^{2 }– 5x + 4 gives (- 3)^{2 }– 5 ( – 3) + 4 = 9 – 15 + 4 = – 2

**Solution:**

Given: x

^{2 }– 5x + 4Now substitute the value of x = -3 in the given equation,

= (-3)

^{2 }– 5(-3) + 4= 9 + 15 + 4

= 28

So the correct solution of x

^{2 }– 5x + 4 = 28

### (c) x^{2}+ 5x gives (- 3)^{2}+ 5 (-3) = – 9 – 15 = – 24

**Solution:**

Given: x

^{2 }+ 5xNow substitute the value of x = -3 in the given equation,

= (-3)

^{2 }+ 5(-3)= 9 – 15

= -6

So the correct solution of x

^{2 }+ 5x = -6

### Question 11. (y – 3)^{2 }= y^{2 }– 9

**Solution:**

Given: (y – 3)

^{2 }= y^{2 }– 9Now we check if the given statement is correct or not

Taking L.H.S:

= (y – 3)

^{2}= y

^{2}– 6y + 9L.H.S ≠ R.H.S

So, the correct solution of (y – 3)

^{2 }= y^{2}– 6y + 9

### Question 12. (z + 5)^{2 }= z^{2 }+ 25

**Solution:**

Given: (z + 5)

^{2 }= z^{2}+ 25Now we check if the given statement is correct or not

Taking L.H.S:

= (z + 5)

^{2}= z

^{2 }+ 10z + 25L.H.S ≠ R.H.S

So, the correct solution of (z + 5)

^{2 }= z^{2 }+ 10z + 25

### Question 13. (2a + 3b) (a – b) = 2a^{2 }– 3b^{2}

**Solution:**

Given: (2a + 3b) (a – b) = 2a

^{2 }– 3b^{2}Now we check if the given statement is correct or not

Taking L.H.S:

= (2a + 3b) (a – b)

= 2a

^{2 }– 2ab + 3ab – 3b^{2 }= 2a

^{2 }– 3b^{2 }+ abL.H.S ≠ R.H.S

So, the correct solution of (2a + 3b) (a – b) = 2a

^{2 }– 3b^{2 }+ ab

### Question 14. (a + 4) (a + 2) = a^{2 }+ 8

**Solution:**

Given: (a + 4) (a + 2) = a

^{2 }+ 8Now we check if the given statement is correct or not

Taking L.H.S:

= (a + 4) (a + 2)

= a

^{2 }+ 2a + 4a + 8^{ }= a

^{2 }+ 6a + 8L.H.S ≠ R.H.S

So, the correct solution of (a + 4) (a + 2) = a

^{2 }+ 6a + 8

### Question 15. (a – 4) (a – 2) = a^{2 }– 8

**Solution:**

Given: (a – 4) (a – 2) = a

^{2 }– 8Now we check if the given statement is correct or not

Taking L.H.S:

= (a – 4) (a – 2)

= a

^{2 }– 2a – 4a + 8^{ }= a

^{2 }– 6a + 8L.H.S ≠ R.H.S

So, the correct solution of (a – 4) (a – 2) = a

^{2 }– 6a + 8

### Question 16. 3x^{2}/3x^{2} = 0

**Solution:**

Given: 3x

^{2}/3x^{2}= 0Now we check if the given statement is correct or not

Taking L.H.S:

= 3x

^{2}/3x^{2}= 1

L.H.S ≠ R.H.S

So, the correct solution of 3x

^{2}/3x^{2}= 1

### Question 17. (3x^{2 }+ 1)/(3x^{2}) = 1 + 1 = 2

**Solution:**

Given: (3x

^{2 }+ 1)/(3x^{2}) = 1 + 1 = 2Now we check if the given statement is correct or not

Taking L.H.S:

= (3x

^{2 }+ 1)/(3x^{2})= 3x

^{2}/(3x^{2})^{ }+ 1/(3x^{2})= 1 + 1/(3x

^{2})L.H.S ≠ R.H.S

So, the correct solution of (3x

^{2 }+ 1)/(3x^{2}) = 1 + 1/(3x^{2})

### Question 18. (3x)/(3x + 2) = 1/2

**Solution:**

Given: (3x)/(3x + 2) = 1/2

Here, L.H.S ≠ R.H.S

So, the correct solution of (3x)/(3x + 2) = (3x)/(3x + 2)

### Question 19. 3/(4x + 3) = 1/4x

**Solution:**

Given: 3/(4x + 3) = 1/4x

Here, L.H.S ≠ R.H.S

So, the correct solution of 3/(4x + 3) = 3/(4x + 3)

### Question 20. (4x + 5)/(4x) = 5

**Solution:**

Given: (4x + 5)/(4x) = 5

Now we check if the given statement is correct or not

Taking L.H.S:

= (4x + 5)/(4x)

= (4x/4x) + 5/4x)

= 1 + 5/4x

L.H.S ≠ R.H.S

So, the correct solution of (4x + 5)/(4x) = 1 + 5/4x

### Question 21. (7x + 5)/5 = 7x

**Solution:**

Given: (7x + 5)/5 = 7x

Now we check if the given statement is correct or not

Taking L.H.S:

= (7x + 5)/5

= (7x/5) + 5/5)

= 7x/5 + 1

L.H.S ≠ R.H.S

So, the correct solution of (7x + 5)/5 = 7x/5 + 1

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