### Home > CCG > Chapter 12 > Lesson 12.2.1 > Problem12-65

12-65.

For each equation below, decide if the equation has any real number for the given variable. For each problem, explain how you know.

1. $4(x - 3) = 11$

Solve for $x$.
Is your solution a real number?

$4(x - 3) = 11$
$\underline{\:\:\:\:\:\:\:\:\div4\:\:\:\:\:\div4}$
$x - 3 = \frac{11}{4}$
$x = \frac{23}{4}$

2. $x^2 = −10$

Is it possible for the square or absolute value of a number to be negative?

No real solution, $x^2$ must be positive or zero.

3. $3x^2 − 18 = 0$

Refer to part (a) for help.

4. $-7 = \vert x - 6 \vert$

Refer to part (b) for help.