EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION |...
12
EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION | x – 5 | = 7 x – 5 = – 7 or x – 5 = 7 x = 5 – 7 or x = 5 + 7 x = –2 or x = 12 Write original equation. Write equivalent equations. Solve for x. Simplify.
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Transcript of EXAMPLE 1 Solve a simple absolute value equation Solve |x – 5| = 7. Graph the solution. SOLUTION |...
EXAMPLE 1 Solve a simple absolute value equation
Solve |x – 5| = 7. Graph the solution.
SOLUTION
| x – 5 | = 7
x – 5 = – 7 or x – 5 = 7
x = 5 – 7 or x = 5 + 7
x = –2 or x = 12
Write original equation.
Write equivalent equations.
Solve for x.
Simplify.
EXAMPLE 1
The solutions are –2 and 12. These are the values of x that are 7 units away from 5 on a number line. The graph is shown below.
ANSWER
Solve a simple absolute value equation
EXAMPLE 2 Solve an absolute value equation
| 5x – 10 | = 45
5x – 10 = 45 or 5x – 10 = –45
5x = 55 or 5x = –35
x = 11 or x = –7
Write original equation.
Expression can equal 45 or –45 .
Add 10 to each side.
Divide each side by 5.
Solve |5x – 10 | = 45.
SOLUTION
EXAMPLE 2 Solve an absolute value equation
The solutions are 11 and –7. Check these in the original equation.
ANSWER
Check:| 5x – 10 | = 45
| 5(11) – 10 | = 45?
|45| = 45?
45 = 45
| 5x – 10 | = 45
| 5(–7) – 10 | = 45?
45 = 45
| – 45| = 45?
EXAMPLE 3
| 2x + 12 | = 4x
2x + 12 = 4x or 2x + 12 = – 4x
12 = 2x or 12 = –6x
6 = x or –2 = x
Write original equation.
Expression can equal 4x or – 4 x
Add –2x to each side.
Solve |2x + 12 | = 4x. Check for extraneous solutions.
SOLUTION
Solve for x.
Check for extraneous solutions
EXAMPLE 3
| 2x + 12 | = 4x
| 2(–2) +12 | = 4(–2)?
|8| = – 8?
8 = –8
Check the apparent solutions to see if either is extraneous.
Check for extraneous solutions
| 2x + 12 | = 4x
| 2(6) +12 | = 4(6)?
|24| = 24?
24 = 24
The solution is 6. Reject –2 because it is an extraneous solution.
ANSWER
CHECK
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
1. | x | = 5
for Examples 1, 2 and 3
The solutions are –5 and 5. These are the values of x that are 5 units away from 0 on a number line. The graph is shown below.
ANSWER
– 3
– 4
– 2
– 1
0
1 2
3
4
5
6
7
– 5
– 6
– 7
5 5
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
2. |x – 3| = 10
for Examples 1, 2 and 3
The solutions are –7 and 13. These are the values of x that are 10 units away from 3 on a number line. The graph is shown below.
ANSWER
– 3
– 4
– 2
– 1
0
1
2
3
4
5
6
7
– 5
– 6
– 7
8
9
10
11
12
13
10 10
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
3. |x + 2| = 7
for Examples 1, 2 and 3
The solutions are –9 and 5. These are the values of x that are 7 units away from – 2 on a number line.
ANSWER
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
4. |3x – 2| = 13
for Examples 1, 2 and 3
ANSWER
The solutions are 5 and .
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
5. |2x + 5| = 3x
for Examples 1, 2 and 3
The solution of is 5. Reject 1 because it is an extraneous solution.
ANSWER
GUIDED PRACTICE
Solve the equation. Check for extraneous solutions.
6. |4x – 1| = 2x + 9
for Examples 1, 2 and 3
ANSWER
The solutions are – and 5. 311
