Question

# Classify the equation 6(x + 2)= 5(x + 7) as having one solution , no solution or infinitely many solutions ?

Hint:

### When a given equation has only 1 value that can be substituted for the variable which will satisfy the given equation, the said equation has only 1 solution. i.e. after simplifying the equation, we will get a single value as the solution for x.

We will simplify the given equation and the number of values we get for the variable.

## The correct answer is: The given equation i.e. 6 (x + 2) = 5 (x + 7) can be classified as an equation with only one solution.

### Step-by-step solution:-

Simplifying the given equation i.e. 6(x+2)= 5(x+7), we get-

6(x+2) = 5(x+7)

∴ 6x + 12 = 5x + 35 .................................. (Simplifying both the sides by opening the brackets and multiplying the expressions)

∴ 6x - 5x = 35 - 12 ................................... (Taking variables and constants on either side of the equation)

∴ x = 23

Since after simplifying the given equation, we get a single value of x i.e. 23 that will satisfy the given equation, we can conclude that the given equation has 1 solution.

Final Answer:-

∴ The given equation i.e. 6 (x + 2) = 5 (x + 7) can be classified as an equation with only one solution.

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Mathematical expressions are made up of at least two numbers or variables, one math operation, and a sentence. This mathematical operation allows you to multiply, divide, add, or subtract numbers.

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1. Arithmetic operators and numbers make up a mathematical numerical expression. There are no symbols for undefined variables, equality, or inequality.

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