CPM Homework Help : CCG Problem 12-65

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Home > CCG > Chapter 12 > Lesson 12.2.1 > Problem 12-65

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.

$4\left(x-3\right)=11$
Hint: (a)
Solve for $x$ .
Is your solution a real number?
Solution (a):
$\begin{array}{r} 4\left(x-3\right) = 11 \\ \div 4 \quad \div 4 \\ \hline x - 3 = \frac{11}{4} \\ x = \frac{23}{4} \end{array}$

$x^2=-10$
Hint (b):
Is it possible for the square or absolute value of a number to be negative?
Answer (b):
No real solution, $x^2$ must be positive or zero.

$3x^2-18=0$
Hint (c):
Refer to part (a) for help.

$-7=\left|x-6\right|$
Hint (d):
Refer to part (b) for help.

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