Maths-

General

Easy

Question

# Determine the number of solutions for each equation:

a)x+3+7= 2x-10-x

Hint:

### 1. 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.

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

3. When after simplifying the equation, we get a single value for the variable in the equation, the equation is said to have only 1 solution.

## The correct answer is: The given equations a)x + 3 + 7= 2x-10-x; b)3(x+4)= 3x+12 and c)5x+8= 2x-1 have No solution, Infinitely many solutions and 1 solution, respectively.

### Step-by-step solution:-

a)x+3+7= 2x-10-x

Simplifying the given equation i.e. x+3+7= 2x - 10 - x, we get-

x + 3 + 7 = 2x - 10 - x

∴ x - 2x + x = - 10 - 3 - 7

∴ 0 ≠ - 20

∴ LHS ≠ RHS

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

b)3(x+4)= 3x + 12

Simplifying the given equation i.e. 3(x+4)= 3x + 12, we get-

3 (x + 4) = 3x + 12

∴ 3x + 12 = 3x + 12

∴ LHS = RHS

Since, after simplifying the above equation, we get both sides of the equation equal to each other, the given equation has infinitely many solutions.

c)5x + 8 = 2x - 1

Simplifying the given equation i.e. 5x + 8 = 2x - 1, we get-

5x + 8 = 2x - 1

∴ 5x - 2x = - 1 - 8 .............................. (Taking variables and constants on either sides of the equation)

∴ 3x = -9

∴ x = - 3 ................................. (Dividing both sides by 3)

Since after simplifying the given equation, we get a single value of x i.e. -3 that will satisfy the given equation, we can conclude that the given equation has 1 solution.

Final Answer:-

∴ The given equations a)x + 3 + 7= 2x-10-x; b)3(x+4)= 3x+12 and c)5x+8= 2x-1 have No solution, Infinitely many solutions and 1 solution, respectively.

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