Question

# Check, whether the following equation has exactly one solution or infinitely many solution or no solution. 4x - 5 = 2(2x - 1) – 3

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 4x - 5 = 2(2x - 1) - 3 has Infinitely Many Solutions

### Step-by-step solution:-

Simplifying the given equation i.e. 4x - 5 = 2(2x - 1) – 3, we get-

4x - 5 = 2(2x - 1) - 3

∴ 4x - 5 = 4x - 2 - 3 ...................................... (Opening the bracket and multiplying 2 with the entire expression on RHS)

∴ 4x - 4x = -2 - 3 + 5 ....................................... (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 4x - 5 = 2(2x - 1) - 3 has Infinitely Many Solutions.

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The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.**Let's take an example:**

Assume the hours are "h" when attempting to equalize,

As per the given question, we can write the equation as:

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### The Price of Stock A at 9 A.M was 12.73 .Since then the price has been increasing at the rate of Rs 0.06 per hour. At noon , the price of stock B was Rs 13.48 .It begins to decrease at the rate of Rs 0.14 per hour. If the stocks continue to increase and decrease at the same rates, in how many hours will the prices of the stocks be the same?

The equation is defined as a mathematical statement with at least two terms containing variables or numbers that are equal.**Let's take an example:**

Assume the hours are "h" when attempting to equalize,

As per the given question, we can write the equation as:

12.73 + 0.06h = 13.48 - 0.14h

Rearrange the terms of h in the above equation,

0.06h + 0.14h = 13.48- 12.73

In the above equation, combine the corresponding terms,

0.2h = 0.75

Divide both sides by 0.2

h = 0.75/0.2

h = 3.75

Thus, the stock prices will be the same in 3.75 hours.