Question

Write an equation with a variable on both sides of the equal sign that has indefinitely many solutions. Solve the equation and explain why it has an infinite number of solutions

Answer 1

5x + 3 - 4x = 3 + x

Combine like terms on both sides of the equation.
5x + 3 - 4x = 3 + x What to do: (5x + 4x =1x or just x)
x + 3 = 3 + x

Isolate the x term by subtracting x from both sides
x + 3 = 3 + x
-x - x
————————
3=3

Since 3 does, in fact, equal 3, it implies there are an infinite number of solutions to this equation. The solution can be written as indefinite solutions or all real numbers.

Answer 2

See below

Explanation:

Many answers 3x + 2 = 2x + x + 2

combine like terms

3x + 2 = 3x + 2 Subtract 3x from both sides

2 = 2

This means that there are infinite solutions. Any number that I replace x with will make a true statement.

Lett's say x = 5

3x + 2 = 2x + x + 2

3(5) + 2 = 2(5) + 5 + 2

15 + 2 = 10 + 5 + 2

17 = 17

What if we try 10?

3x + 2 = 2x + x + 2

3(10) + 2 = 2(10) + 10 + 2

30 + 2 = 20 + 10 + 2

32 = 32

When I combine the like terms the left side looks just like the right side.

3x + 2 = 2x + x + 2

3x + 2 = 3x + 2. Any number that I put in for x will work.