Home > INT3 > Chapter 12 > Lesson 12.1.1 > Problem12-5

12-5.

Decide if each of the following equations is always true, sometimes true, or never true. If an equation is always true, justify how you know; if it is sometimes true, give the exact values of $x$ that make it true; and if it is never true, explain why it is never true.

1. $3x – 2 – 4\left(x + 1\right) = –x – 6$

Simplify the part of the equation on the left side of the equals sign.
Does it equal the part on the right side?

Always.

1. $3x – 5 = 2\left(x + 1\right) + x$

Use the same method as part (a).

1. $\sin(x)=\cos(\frac{\pi}{2}-x)$

Substitute values into the equations for $x$.
Are they always equal?

Always.

1. $\tan(x)=1$

Is this always true?
If not, what values of $x$ would make it true?