Maths-

General

Easy

Question

# Solve the following equation : 2(1 - x) + 5x = 3(x + 1) and say whether it is having one solution , no solution or infinitely many solutions ?

Hint:

### An equation where no value can be substituted for the variable which will satisfy the equation i.e. for no value of x (or any other variable in the equation), would LHS equal RHS.

Hence, an equation where LHS ≠ RHS for any value of x has no solutions.

We will simplify the given equation and check whether LHS = RHS or not.

## The correct answer is: The given equation 2(1 - x) + 5x = 3(x + 1) can be classified as having no solution

### Step-by-step solution:-

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

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

∴ 2 - 2x + 5x = 3x + 3

∴ -2x + 5x - 3x = 3 - 2

∴ 0 ≠ 1

∴ LHS ≠ RHS

Since in the above equation, LHS is not equal to RHS, the given equation has no solutions.

Final Answer:-

∴ The given equation 2(1 - x) + 5x = 3(x + 1) can be classified as having no solution.

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