### Home > AC > Chapter 14 > Lesson 14.3.1.1 > Problem3-9

3-9.

If two expressions are equivalent, they can form an equation that is considered to be always true. For example, since $3(x − 5)$ is equivalent to $3x −15$, then the equation $3(x − 5) = 3x − 15$ is always true, or true for any value of $x$.

If two expressions are equal only for certain values of the variable, they can form an equation that is considered to be sometimes true. For example, $x + 2$ is equal to $3x − 8$ only when $x = 5$, so the equation $x + 2 = 3x − 8$ is said to be sometimes true.

If two expressions are not equal for any value of the variable, they can form an equation that is considered to be never true. For example, $x − 5$ is not equal to $x + 1$ for any value of $x$, so the equation $x − 5 = x + 1$ is said to be never true.

Is the equation $(x+3)^2=x^2+9$ always, sometimes or never true? Justify your reasoning completely. Homework Help ✎

Solve the equation. Rewrite $(x + 3)²$ as $(x+3)(x+3)$ to begin.

The equation is sometimes true; it is only true when $x=0$.