Home > GB8I > Chapter 1 Unit 1 > Lesson INT1: 1.1.2 > Problem1-16

1-16.

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

1.  $x + 5 = 5$

1.  $2 x - 6 = 3 x + 1 - x - 7$

Combine like terms on both sides of the equation.
$2x−6=2x−6$

Add $6$ to both sides
$2x−6=2x−6$
$\ \ \ \ \ +6\ \ \ \ \ \ \ \ \ +6$
$2x=2x+0$
$2x=2x$

$x$ can equal any number. Do you understand why?

1.  $3 x + 1 = 43$

• Subtract $1$ from each side.
$3x+1=43$
$\ \ \ \ −1\ \ \ \ −1$
$3x=42$

Divide each side by $3$.

$\frac{3x}{3}=\frac{42}{3}$

$x=14$

1.  $4 x - 1 = 4 x + 7$

• If there is no variable in the final equation, what does that tell you about the final solution?