How do you solve #10 - |x + 2| = 12#?

Question

Eva Adamson · Accepted Answer

This equation has no solutions. See explanation for details.

To solve this equation first we have to move #10# to the right side to leave absolute value alone on the left side. #10-|x+2|=12# #-|x+2|=2# Now we can multiply both sides by #-1# to get rid of minus sign in front of absolute value. #|x+2|=-2# Since an expression's absolute value cannot be negative, there are no solutions to this equation, just as there are none to the original.

Julia Adams · Answer

undefined To solve the equation 10 - |x + 2| = 12, you would follow these steps:

1. Add |x + 2| to both sides: 10 = |x + 2| + 12
2. Subtract 12 from both sides: -2 = |x + 2|
3. Since the absolute value of a number is always non-negative, -2 cannot be the absolute value of a number. Therefore, there is no solution to the equation.

Eli Assouline · Answer

undefined To solve the equation 10 - |x + 2| = 12, follow these steps:

1. Add |x + 2| to both sides of the equation to isolate the absolute value term.
2. Subtract 10 from both sides.
3. Divide both sides by -1 to make the absolute value term positive.
4. Solve for x by considering two cases: when the expression inside the absolute value is positive and when it's negative.
5. Solve each case separately and check for extraneous solutions.

The solutions to the equation are the values of x that satisfy the given equation.