1

Write the equation \(6 = 4 x  7\) as two separate equations. Neither of your equations should use absolute value.
Solve both equations above.
2

Write the equation \(7 = 6 x  5\) as two separate equations. Neither of your equations should use absolute value.
Solve both equations above.
3

Write the equation \(\displaystyle \left 2  \frac{r}{3} \right = 5\) as two separate equations. Neither of your equations should use absolute value.
Solve both equations above.
4

Write the equation \(\displaystyle \left 2  \frac{r}{7} \right = 5\) as two separate equations. Neither of your equations should use absolute value.
Solve both equations above.
5
Verify that the value \(1\) is a solution to the absolute value equation \(\abs{\frac{x3}{2}}=2\text{.}\)
Verify that the value \(\frac{2}{3}\) is a solution to the absolute value equation \(\abs{6x5}\lt 4\text{.}\)
6
Verify that the value \(8\) is a solution to the absolute value equation \(\abs{\frac{1}{2}x2}=2\text{.}\)
Verify that the value \(6\) is a solution to the absolute value equation \(\abs{72x}\ge 5\text{.}\)
7
Solve the following equation.
\(\displaystyle{ \left\lvert 3 x+ 8 \right\rvert = 7 }\)
8
Solve the following equation.
\(\displaystyle{ \left\lvert 4 x  7 \right\rvert = 4 }\)
9
Solve the equation \(\left\lvert 3 x + 3\right\rvert =17\text{.}\)
10
Solve the equation \(\left\lvert 4 x  3\right\rvert =18\text{.}\)
11
Solve: \(\left\lvert x \right\rvert = 2\)
12
Solve: \(\left\lvert x \right\rvert = 10\)
13
Solve: \(\left\lvert y  3 \right\rvert = 11\)
14
Solve: \(\left\lvert a  1 \right\rvert = 17\)
15
Solve: \(\left\lvert 2a + 5 \right\rvert = 11\)
16
Solve: \(\left\lvert 2b + 3 \right\rvert = 15\)
17
Solve: \(\displaystyle \left\lvert\frac{2 b  1}{3}\right\rvert = 3\)
18
Solve: \(\displaystyle \left\lvert\frac{2 t  5}{5}\right\rvert = 3\)
19
Solve: \(\left\lvert t \right\rvert = 8\)
20
Solve: \(\left\lvert x \right\rvert = 4\)
21
Solve: \(\left\lvert x + 4 \right\rvert = 0\)
22
Solve: \(\left\lvert y + 2 \right\rvert = 0\)
23
Solve: \(\left\lvert 4  3a \right\rvert = 10\)
24
Solve: \(\left\lvert 4  3a \right\rvert = 14\)
25
Solve: \(\left\lvert\frac{1}{2}b + 5\right\rvert = 3\)
26
Solve: \(\left\lvert\frac{1}{4}b + 7\right\rvert = 3\)
27
Solve: \(\left\lvert0.5 0.2t\right\rvert = 1\)
28
Solve: \(\left\lvert0.2 0.5t\right\rvert = 4\)
29
Solve: \(\left\lvert x + 9\right\rvert  2 = 4\)
30
Solve: \(\left\lvert x + 5\right\rvert  4 = 2\)
31
Solve: \(\left\lvert2 y  10\right\rvert + 8 = 8\)
32
Solve: \(\left\lvert5 a  10\right\rvert + 6 = 6\)
33
Solve: \(\left\lvert a + 5 \right\rvert + 9 = 6\)
34
Solve: \(\left\lvert b + 1 \right\rvert + 3 = 2\)
35
Solve: \(\left\lvert 2 b + 7\right\rvert + 9 = 4\)
36
Solve: \(\left\lvert 8 t + 5\right\rvert + 9 = 6\)
37
Solve the equation by inspection (meaning in your head).
\(\displaystyle{\left\lvert 6x + 12\right\rvert = 0 }\)
38
Solve the equation by inspection (meaning in your head).
\(\displaystyle{\left\lvert 6x + 24\right\rvert = 0 }\)
39
The equation \(\lvert x\rvert =\lvert y\rvert\) is satisfied if \(x=y\) or \(x=y\text{.}\) Use this fact to solve the following equation.
\(\displaystyle{\left\lvert {3x1} \right\rvert = \left\lvert {2x+2} \right\rvert}\)
40
The equation \(\lvert x\rvert =\lvert y\rvert\) is satisfied if \(x=y\) or \(x=y\text{.}\) Use this fact to solve the following equation.
\(\displaystyle{\left\lvert {4x4} \right\rvert = \left\lvert {x+4} \right\rvert}\)
41
The equation \(\lvert x\rvert =\lvert y\rvert\) is satisfied if \(x=y\) or \(x=y\text{.}\) Use this fact to solve the following equation.
\(\displaystyle{\left\lvert x + 2 \right\rvert = \left\lvert x  1 \right\rvert}\)
42
The equation \(\lvert x\rvert =\lvert y\rvert\) is satisfied if \(x=y\) or \(x=y\text{.}\) Use this fact to solve the following equation.
\(\displaystyle{\left\lvert x + 2 \right\rvert = \left\lvert x  3 \right\rvert}\)
43
Solve the equation: \(\displaystyle{ \left\lvert 2 x  9 \right\rvert = \left\lvert 9 x + 7\right\rvert }\)
44
Solve the equation: \(\displaystyle{ \left\lvert 4 x  7 \right\rvert = \left\lvert 5 x + 4\right\rvert }\)
45
Solve the following equation.
\(\displaystyle{\left\lvert 3 x  4 \right\rvert = \left\lvert9 x  9\right\rvert }\)
46
Solve the following equation.
\(\displaystyle{\left\lvert 3 x + 9 \right\rvert = \left\lvert6 x +6\right\rvert }\)