Question

# Classify the equation 170x- 1000= 30 ( 5x - 30 ) 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. 170x - 1000 = 30 (5x - 30) can be classified as an equation with only one solution

### Step-by-step solution:-

Simplifying the given equation i.e. 170x - 1000 = 30 (5x - 30), we get-

170x - 1000 = 30 (5x - 30)

∴ 170x - 1000 = 150x - 900 .................................. (Opening the bracket and multiplying 30 with the entire expression on RHS)

∴ 170x - 150x = -900 + 1000 ................................. (Taking variables and constants on either side of the equation)

∴ 20x = 100

∴ x = 5 ............................................... (Dividing both sides by 20)

Since after simplifying the given equation, we get a single value of x i.e. 5 that will satisfy the given equation, we can conclude that the given equation has 1 solution.

Final Answer:-

∴ The given equation i.e. 170x - 1000 = 30 (5x - 30) can be classified as an equation with only one solution.

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2. Unknown variables, numerical values, and arithmetic operators make up an algebraic expression. There are no symbols for equality or inequality in it.

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