Question

1.) Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.

2.) Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation.

3.) Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation

Answer 1

9514 1404 393

Answer:

1. x = x+1
2. 0 = x+1
3. x+1 = x+1

Explanation:

1. There will be no solution if the equation is a contradiction. Usually, it is something that can be reduced to 0 = 1.

If we choose to make our equation ...

x = x +1

Subtracting x from both sides of the equation gives ...

0 = 1

There is no value of the variable that will make this be true.

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2. Something that reduces to x = c will have one solution. One such equation is ...

0 = x+1

x = -1 . . . . subtract 1 from both sides

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3. Something that reduces to x = x will have an infinite number of solutions.

One such equation is ...

x+1 = x+1

Subtracting 1 from both sides gives ...

x = x . . . . true for all values of x