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ake sure that you attend the Live Lesson or watch the recording to help answer the questions.Click Here for Graphing Calculator Video and 8th Grade Math & Algebra Graphing CalculatorGrade 8 Mathematics Formula SheetWhen 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)ResponsesThere 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 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 no solution to this equation because there are the same number of x's on both sides of the equation, but a different constant.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.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.

1 answer

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

  1. Start by subtracting \(4x\) from both sides: \[ 18 = 5 \]

  2. This statement, \(18 = 5\), is clearly false.

Now, let’s analyze the options provided:

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

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

  • 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. (Correct)

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

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.