CPM Homework Help : GB8I Problem 1-16

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1-16.

What value(s) of $x$ will make each equation below true?

$x + 5 = 5$

Hint (a):
This one you can do in your head.

$2 x - 6 = 3 x + 1 - x - 7$
Step 1(b):
Combine like terms on both sides of the equation.
$2x−6=2x−6$
Step 2(b):
Add $6$ to both sides
$2x−6=2x−6$
$\ \ \ \ \ +6\ \ \ \ \ \ \ \ \ +6$
$2x=2x+0$
$2x=2x$
Answer (b):
$x$ can equal any number. Do you understand why?

$3 x + 1 = 43$

Step 1(c):
Subtract $1$ from each side.
$3x+1=43$
$\ \ \ \ −1\ \ \ \ −1$
$3x=42$
Step 2(c):
Divide each side by $3$ .
$\frac{3x}{3}=\frac{42}{3}$
Answer (c):
$x=14$

$4 x - 1 = 4 x + 7$

Hint (d):
If there is no variable in the final equation, what does that tell you about the final solution?

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