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When you see an equation such as: 4x+18=4x+5

you can tell how many solutions it will have for x.

Which is a good explanation of how you can tell?

(1 point)
Responses

You cannot tell the number of solutions to a linear equation in one variable without graphing it.
You cannot tell the number of solutions to a linear equation in one variable without graphing it.

There are infinite solutions to this equations because there are the same number of x's on both sides of the equation and the same constant.
There are infinite solutions to this equations because there are the same number of x's on both sides of the equation and the same constant.

There is one solution for x to this equation because there are the same number of x's on both sides of the equation.
There is one solution for x to this equation because there are the same number of x's on both sides of the equation.

There is no solution to this equation because there are the same number of x's on both sides of the equation, but a different constant.

1 answer

To determine the number of solutions for the equation \(4x + 18 = 4x + 5\), we can simplify both sides of the equation.

  1. Start with the equation: \[ 4x + 18 = 4x + 5 \]

  2. Subtract \(4x\) from both sides: \[ 18 = 5 \]

This statement is clearly false, which indicates that there is no value of \(x\) that can satisfy the equation. Therefore, the correct explanation is:

There is no solution to this equation because there are the same number of x's on both sides of the equation, but a different constant.

This means that the equation is inconsistent.