### Home > INT2 > Chapter 10 > Lesson 10.1.3 > Problem10-45

10-45.

Decide how many real solutions each equation below has. Explain how you know. You may not need to solve the equation.

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

Can you easily solve for $x$ and find an answer?

How many $x$ values are possible?

One solution. What is your explanation?

2. $x^2 = -10$

Try solving for $x$ by square-rooting each side.
What do you notice?

3. $3x^2 - 18 = 0$

See hints from part (a).

4. $-7 =| x - 6 |$

What type of number does an absolute value sign make? Positive or negative?

No solution; Absolute value must be positive or zero.