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Question: How much solution does the equation \[ - 4(x + 5) = - 4x - 20\] have?...

How much solution does the equation −4(x+5)=−4x−20 - 4(x + 5) = - 4x - 20 have?

Explanation

Solution

For finding values of variable in a given linear equation you have to simplify the equation by putting constant term aside and variable term in one side, for number of solution you should have to see with the solutions which are satisfying the given equation, it may be one or two or infinite also.

Complete step by step solution:
For the given equation −4(x+5)=−4x−20 - 4(x + 5) = - 4x - 20

We get that the left hand value of the equation is equal to the right hand value of the equation that means for every value of “x” both sides of equal sign are satisfying each other, which shows us that the given equation has an infinite number of solutions.

⇒−4(x+5)=−4x−20 ⇒−4x−20=−4x−20 \Rightarrow - 4(x + 5) = - 4x - 20 \\\ \Rightarrow - 4x - 20 = - 4x - 20 \\\

So our required answer for the number of solutions the given equation is having is infinite.

Additional Information: Here when you solve the equation you will get the result as zero equals zero that means both side of equal sign are having the same thing only some adjustment are taken into hand which makes the equation have a different look, but the results are same,

Note: In such question when you have to get the number of solutions then you have to solve the equation first, and making the variable term in one side and the constants on the other side you can solve the question, but here things are different you can see that on the both sides of the equation same things are written so you have to check for the different values.