Maths-

General

Easy

Question

# Solve 4(4x + 3)= 19x + 9 - 3x + 3 . Does the equation have one solution , no solution or infinitely many solutions ?

Hint:

### When Both sides of an equation are equal, the said equation is said to have infinitely many solutions.

i.e. When LHS = RHS, the given equation has infinitely many solutions.

## The correct answer is: The given equation 4 (4x + 3) = 19x + 9 - 3x + 3 has Infinitely Many Solutions

### Step-by-step solution:-

Simplifying the given equation i.e. 4(4x + 3) = 19x + 9 - 3x + 3, we get-

4(4x + 3) = 19x + 9 - 3x + 3

∴ 16x + 12 = 19x + 9 - 3x + 3 ...................................... (Opening the bracket and multiplying 4 with the entire expression on LHS)

∴ 16x - 19x + 3x = 9 + 3 - 12 ....................................... (Taking variables and constants on either sides of the equation)

∴ 0 = 0

∴ LHS = RHS

Since in the above equation, LHS is equal to RHS, the given equation has Infinitely Many Solutions.

Final Answer:-

∴ The given equation 4 (4x + 3) = 19x + 9 - 3x + 3 has Infinitely Many Solutions.

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