Absolute Value Problem?I dont know how to find each value!!-7|x+2|=49and|10|?

Answer 1

7|x+2|=49
divide both sides by 7
|x+2|=7
absolute value always has two answers
for this particular one,
x+2=7 and -x-2=7
x=5 and x=-9
{5, -9}

Absolute value asks for the positive value of what is inside the | |. This is why for the problem above, we said -x-2 and x+2....the absolute value of both of those is x+2.

I do not know if you said that the equation has 2 solutions or if they are separate, so I will do both for you.

If the equation has two solutions: 7|x+2|=|10|
aka 7|x+2|=10
aka |x+2|=10/7
meaning
x+2=10/7 and -x-2=10/7
x=-4/7 and x=-24/7
{-4/7, -24/7}
If the two are combined, your full solution set will be
{-9, -24/7, -4/7, 5}


If |10| problem is separate: the positive of 10 is 10, so your answer is 10.

Answer 2

7|x+2| = 49
=>|x+2| = 7
=> x+2 = ±7
=> x = -9, 5

7|x+2| = 10
=> x+2 = ±10/7
=> x = -4/7, -24/7

Answer 3

Absolute Value Problem?I dont know how to find each value!!
1) -7|x+2|=49 ----> |x +2| = -7 ( no solutions as absolute values are non negative)
and
2) -7|x +2| = |10| , same reasoning, no solutions.

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Why are the rest of the people answering different questions when it is clearly written as

-7|x+2 = ..., not "plus 7|x+2| "

Answer 4

7|x+2|=49
case 1: x+2 > 0 ; |x+2|=x+2
7(x+2)=49
7x+14=49
7x=35
x=5
case 2: x+2 < 0 ; |x+2| = -x-2
7(-x-2)=49
-7x-14=49
-7x=63
x=-9
x=-9 , x=5

|10|=10
Use the same procedure (consider 2 cases > 0 and < 0) and solve
7|x+2|=10

Answer 5

Divide by -7
abs(x+2)=-7 this is not possible since the absolute value must be nonnegative and the right side is negative.

abs(10)=10

Answer 6

7|x+2|=49
|x+2|= 7
x= 5 or -9

7|x+2|=|10|
|x+2| =|10|/7
x = |10|/7 -2 or -|10|/7 - 2