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Answer:
x = -2 because that is the value that makes the equation true
Explanation:
Minus signs are everywhere. They can all be eliminated by multiplying both sides of the equation by -1.
-1(-x -6 -x) = -1(-2)
(-1)(-x) +(-1)(-6) +(-1)(-x) = 2 . . . . . distribute the -1
x + 6 + x = 2 . . . . . . . . simplify
x + x + 6 = 2 . . . . . . . . rearrange
(1 +1)x +6 = 2 . . . . . . . . factor, using the distributive property
2x +6 = 2 . . . . . . . . . . . simplify
2x +6 -6 = 2 -6 . . . . . . subtract 6 from both sides
2x = -4 . . . . . . . . . . . . . simplify
(2x)/2 = (-4)/2 . . . . . . . divide both sides by 2
x = -2 . . . . . . . . . . . . . . simplify
x is -2 because that is the value we get when we apply the properties of equality to the equation. We can check to see if it works in the original equation.
Check
-x -6 -x = -2
-(-2) -6 -(-2) = -2 . . . . put -2 where x is
2 -6 +2 = -2 . . . . . . . . simplify the signs
-4 +2 = -2 . . . . . . . . . . add the first two terms (could do all at once)
-2 = -2 . . . . . . . . yes, the value of x=-2 makes the equation true
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Additional comment
The properties of equality we're concerned with here are the multiplication property of equality, the addition property of equality and the division property of equality. Respectively, these tell us that multiplying, adding, or dividing both sides of the equation by the same number doesn't change the value of the variable.
These properties are essential to understanding how algebra works.