SAT
Find the solution when an absolute value equals 0. Use Guess and Check with the answer choices.
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Guess and Check
Use Guess and Check with the answer choices.
Substitute each value in the choice for x.
The choice works only when every value gives 0.
Example
|x − 7| = 0
x = −7, |−7 − 7| = |−14| = 14. No, continue.
x = 7, |7 − 7| = |0| = 0. Yes.
Work these three in a session. Use Guess and Check with the answer choices.
|x − 4| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = −4, |−4 − 4| = |−8| = 8. No, continue.
B. x = 0, |0 − 4| = |−4| = 4. No, continue.
C. x = 4, |4 − 4| = |0| = 0. Yes.
D. x = −4 and x = 4, |−4 − 4| = |−8| = 8 and |4 − 4| = |0| = 0. No.
Answer: C. x = 4
|x − 5| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = 5, |5 − 5| = |0| = 0. Yes.
B. x = −5, |−5 − 5| = |−10| = 10. No, continue.
C. x = 0, |0 − 5| = |−5| = 5. No, continue.
D. x = −5 and x = 5, |−5 − 5| = |−10| = 10 and |5 − 5| = |0| = 0. No.
Answer: A. x = 5
|x − 8| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = 0, |0 − 8| = |−8| = 8. No, continue.
B. x = −8 and x = 8, |−8 − 8| = |−16| = 16 and |8 − 8| = |0| = 0. No, continue.
C. x = −8, |−8 − 8| = |−16| = 16. No, continue.
D. x = 8, |8 − 8| = |0| = 0. Yes.
Answer: D. x = 8
Try these five on your own. Use Guess and Check with the answer choices.
|x − 3| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = −3 and x = 3, |−3 − 3| = |−6| = 6 and |3 − 3| = |0| = 0. No, continue.
B. x = 3, |3 − 3| = |0| = 0. Yes.
C. x = −3, |−3 − 3| = |−6| = 6. No, continue.
D. x = 0, |0 − 3| = |−3| = 3. No.
Answer: B. x = 3
|x − 6| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = 0, |0 − 6| = |−6| = 6. No, continue.
B. x = −6, |−6 − 6| = |−12| = 12. No, continue.
C. x = −6 and x = 6, |−6 − 6| = |−12| = 12 and |6 − 6| = |0| = 0. No, continue.
D. x = 6, |6 − 6| = |0| = 0. Yes.
Answer: D. x = 6
|x − 9| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = 9, |9 − 9| = |0| = 0. Yes.
B. x = 0, |0 − 9| = |−9| = 9. No, continue.
C. x = −9 and x = 9, |−9 − 9| = |−18| = 18 and |9 − 9| = |0| = 0. No, continue.
D. x = −9, |−9 − 9| = |−18| = 18. No.
Answer: A. x = 9
|x − 2| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = −2, |−2 − 2| = |−4| = 4. No, continue.
B. x = 2, |2 − 2| = |0| = 0. Yes.
C. x = 0, |0 − 2| = |−2| = 2. No, continue.
D. x = −2 and x = 2, |−2 − 2| = |−4| = 4 and |2 − 2| = |0| = 0. No.
Answer: B. x = 2
|x − 11| = 0
Which choice is the solution to the equation?
Use Guess and Check with the answer choices.
Use Guess and Check with the answer choices.
A. x = −11 and x = 11, |−11 − 11| = |−22| = 22 and |11 − 11| = |0| = 0. No, continue.
B. x = 0, |0 − 11| = |−11| = 11. No, continue.
C. x = 11, |11 − 11| = |0| = 0. Yes.
D. x = −11, |−11 − 11| = |−22| = 22. No.
Answer: C. x = 11
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