|x - 3| = 7 Can you please help me understand this question!?

Question

{x| -4, 4}
{x| -4, 10}
{x| -10, 10}
{x| -10, 4}

Here are my options. Can you please tell me the answer and how you got it! I understand how to get the answer but I dont understand which number goes first if you understand what i mean!

Answer 1

It is asking what numbers are 7 units away from 0 when you subtract 3 from them.

|10-3| = 7
|-4 - 3| = |-7| = 7

So 10 and -4, when you subtract 3 from them, are both 7 units away from 0. One in the positive direction and one in the negative direction.

Answer 2

the answer is {x| -4, 10}

the lines | ... | mean absolute value. Which means whatever is inside the bars is made positive. Example | -3 | = 3, | 4-6 | = 2, | 6-4| = also 2

Now for two different values |X-3| = 7 so we know that -4 - 3 = -7 so |-4 -3| = 7

Narrowing us down to options 1 or 2

also 10 - 3 = 7 so |10 - 3| = 7

basically do the math inside the | ... | first, then make it positive.

Answer 3

when you solve absolute values - think that what is in the absolute value you take as positive and negative ...so you end up with 2 equations that you solve.

Ix-3I = 7

Equation 1:
+(x-3) = 7
x-3=7
x=7+3
x=10

Equation 2:
-(x-3) = 7
-x+3 = 7
-x=7-3
-x=4
x= - 4

So your solution is -4, 10 (answer b)
The way the solution is written is from the smallest to the largest so naturally -4 is smaller than 10. If you look at all the other options, they are not correct, but they do follow the same patters - smaller number, larger number.

Answer 4

it would be the second answer {x -4, 10}, because the the lines on either side of x-3 is the modulus sign, meaning no matter what is inside the modulus sign, the number inside would be a positive number.. and therefore the only answer to satisfy that is the second answer: when x=-4, the answer would be -7, but with the modulus sign the minus disappear, so it would be 7. and when x=10, thats just easy.. 10-3=7!!

Answer 5

The absolute value of (x -3) is 7
so if (x -3) is +ve number
then x -3 = 7
or x = 7 + 3 =10

if (x -3) is -ve number
then x - 3 = -7
x = -7 + 3 = -4

so the answer is {x| -4, 10}

Answer 6

Lets flow the absolute value signs over to the right as a plus or minus. So now we know that x-3=+/-7

Solve for x-3=+7

Solve for x-3=-7

for the first we get that x must be 10, for the second we get that x must be -4, so we end up with the data set {x|-4,10}

Answer 7

|x - 3| = 7
This is the same as:
-7 = x-3 = 7
Add 3 to all terms getting
-4 = x = 10
S0 answer is {x| -4, 10}

Answer 8

just plug in for each one and see if it gives you 7

rememeber if you plug in the absolute value and it gives you the answer -7..it would still work because the absolute value turns the number positive

ps. the answer is {x|-4, 10}
check to know how to do it

Answer 9

The answer is {xl -4,10}
negative four minus 3 is negative seven, so since it's looking for the absolute value, it turns to positive seven.
ten minus 3 is seven, and it stays as seven because all absolute values are positive.

Answer 10

|x - 3| = 7

If |x| = 5, then x = either -5 or +5, for example

|x - 3| = 7

Solve both cases

x - 3 = 7
x = 10

x - 3 = -7
x = -4