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Solve the following equation:
2|x−5|+16=30.
- a)x=0;10
- b)x=2
- c)x=−7;7
- d)x=−9:16
- e)x=−2;12
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
Solve the following equation:2|x−5|+16=30.a)x=0;10b)x=2c)x=&minu...
We start by isolating the absolute value expression:
2|x−5|+16=30⇔2|x−5|=30−16=14⇔|x−5|=7
This gives us two cases when we remove the absolute value:
x−5=7 and x−5=−7
Then we solve for each case:
x−5=7⇒x=7+5⇒x=12
x−5=−7⇒x=−7+5⇒x=−2
Most Upvoted Answer
Solve the following equation:2|x−5|+16=30.a)x=0;10b)x=2c)x=&minu...
Understanding the Equation
To solve the equation 2|x - 5| + 16 = 30, we will isolate the absolute value term.
Step 1: Isolate the Absolute Value
- Subtract 16 from both sides:
2|x - 5| = 14
- Now, divide both sides by 2:
|x - 5| = 7
Step 2: Solve the Absolute Value Equation
The equation |x - 5| = 7 leads to two cases:
1. Case 1: x - 5 = 7
- Add 5 to both sides:
- x = 12
2. Case 2: x - 5 = -7
- Add 5 to both sides:
- x = -2
Conclusion: Solutions
The solutions to the equation are:
- x = 12
- x = -2
Thus, the correct answer is option 'E', which states x = -2; 12.
Final Result
Therefore, the values of x that satisfy the original equation are:
- x = -2
- x = 12
To solve the equation 2|x - 5| + 16 = 30, we will isolate the absolute value term.
Step 1: Isolate the Absolute Value
- Subtract 16 from both sides:
2|x - 5| = 14
- Now, divide both sides by 2:
|x - 5| = 7
Step 2: Solve the Absolute Value Equation
The equation |x - 5| = 7 leads to two cases:
1. Case 1: x - 5 = 7
- Add 5 to both sides:
- x = 12
2. Case 2: x - 5 = -7
- Add 5 to both sides:
- x = -2
Conclusion: Solutions
The solutions to the equation are:
- x = 12
- x = -2
Thus, the correct answer is option 'E', which states x = -2; 12.
Final Result
Therefore, the values of x that satisfy the original equation are:
- x = -2
- x = 12
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