algebra extra credit

Question

Jillana begins to solve a linear equation that results in a variable expression set equal to the same variable expression. Which is the best interpretation of this solution?

A The equation has one solution: x = 0.

B The equation has one solution: x = 1.

C The equation has no solution.

D The equation has infinite solutions.

Answer 1

a variable expression set equal to the same variable expression

This simply means that what is on the left side of the = looks identical to what is on the right side.

4x - 39 = 4x - 39

When your coefficients are equal AND your constants are equal, your variable can be anything.

As in this case, no matter what value you give to x, the equation will always be true.

Therefore, there is an infinite number of solutions. D.

Note, if your coefficients are equal and your constants are not, there is no solution. 4x + 8 = 4x + 3. There is no number that x can be to make 8 = 3.

Likewise, if your coefficients are different and your constants are equal, the ONLY solution is zero. 9x + 13 = 5x + 13,