Lesson 16: Practice Problems

Problem 1

Lin was looking at the equation $2 x - 32 + 4 (3 x - 2462) = 14 x$ . She said, “I can tell right away there are no solutions, because on the left side, you will have $2 x + 12 x$ and a bunch of constants, but you have just $14 x$ on the right side.” Do you agree with Lin? Explain your reasoning.

Problem 2

Han was looking at the equation $6 x - 4 + 2 (5 x + 2) = 16 x$ . He said, “I can tell right away there are no solutions, because on the left side, you will have $6 x + 10 x$ and a bunch of constants, but you have just $16 x$ on the right side.” Do you agree with Han? Explain your reasoning.

Problem 3

Decide whether each equation is true for all, one, or no values of $x$ .

$6 x - 4 = - 4 + 6 x$
$4 x - 6 = 4 x + 3$
$- 2 x + 4 = - 3 x + 4$

Problem 4 From Unit 4 Lesson 13

Solve each of these equations. Explain or show your reasoning.

$3 (x - 5) = 6$
$2 (x - \frac{2}{3}) = 0$
$4 x - 5 = 2 - x$

Problem 5 From Unit 1 Lesson 6

In the picture triangle $A^{'} B^{'} C^{'}$ is an image of triangle $A B C$ after a rotation. The center of rotation is $E$ .

Quadrilateral A prime, B prime, C prime, D prime is an image of quadrilateral A, B, C, D after rotation around another point, E. Side A prime, B prime has length 9. Angle D has measure 45 degrees.

What is the length of side $A B$ ? Explain how you know.
What is the measure of angle $D^{'}$ ? Explain how you know.

Problem 6

Solve each of these equations. Explain or show your reasoning.

$2 (x + 5) = 3 x + 1$
$3 y - 4 = 6 - 2 y$
$3 (n + 2) = 9 (6 - n)$