Determining if Zero Is a Solution

1.7.1 Determining if Zero Is a Solution

1.7.1 • Determining if Zero Is a Solution

Is 0 a solution of an equation $4 (x + 2) = 10$ ? Explain.

Compare your answer:

No. For example: If $x = 0$ , then the expression on the left has the value 8, which makes the equation false.

Is 0 a solution for the equation $12 - 8 x = 3 (x + 4)$ ? Explain.

Compare your answer:

Yes. For example: Substituting 0 for $x$ gives $12 = 12$ , which is true.

Is 0 a solution for the equation $5 x = \frac{1}{2} x$ ? Explain.

Compare your answer:

Yes. For example: 5 multiplied by 0 is 0, and $\frac{1}{2}$ multiplied by 0 is also 0, so the two sides of the equation are equal.

Is 0 a solution for the equation $\frac{6}{x} + 1 = 8$ ? Explain.

Compare your answer:

No. For example: Dividing by 0 gives an undefined result, so it cannot be added by 1 to equal 8.