How do I solve and graph this equation: |x| (less than or equal to sign) 10??

Question

If the graphing part is to complicated than you can just tell me how to solve it. There are these 2 that I'm not quite sure if I understand either

|x|=8 and |x| > .5

But I figured that x=8 and then x=.5 but I'm still not sure how I graph that.

A- |x|=8 (solve & graph)

B- |x| > .5 (solve & graph)

They are separate problems.

Answer 1

To solve the equation, you would have

-10 < x < 10 (with the line under the < signs for or equal to)

To graph, shade the point at -10 and 10 and all points between.

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For the |x| = 8, the solution is x = 8 or x = -8
The graph would be circles at 8 and at -8

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For the |x| > 5
The solution is x < -5 or x > 5
The graph would be empty circles at -5 and at 5 with the shading to the left of -5 and to the right of 5

Answer 2

|x|=8 this can be solve by |8|=8 and |-8|=8 since abssolute value is the distance of a number from zero. therefore x = 8 and -8
plot the two in a cartesian plane by setting points to (-8,0) and (8, 0)

for the second problem is an inequality problem you need two solutions. |x| > 5, this is solve by
x >5 or x < - 5
then plot the points in a line graph, x > 5 must have an arrow going to right, while x < -5 have an arrow going to the left

Answer 3

I love how everyone tries to help, and everyone gets it just a little wrong. lxl= absolute value of x, so x is the positive or negative of the number indicated. To graph, you only use a single line, where you can put a point at -8 and also at +8, to reference on of your examples. Now with your questions about lxl< or=, this is graphed in a different way. You must indicate a range of numbers on your graph. If lxl= to -10, but <= +10. On your line, it looks like this, solid point at -10 line goes until solid point at positive 10. If you have an equation that just indicates > or <, such as lxl>6, then you need to indicate an open point at 6 and -6. Indicate an ongoing line extending out from -6, because you want all numbers less than -6, and a line extending out from 6, because you want all numbers greater than 6. Hope this makes sense for you, and for everyone else out there who sort of remembers how to do math.

Answer 4

k

for graphing, you would graph the line between 10 and -10 on the numberline...

if there was no equals too, only less then, you would graph the same thing but draw a circle around the points 10 and -10 to show that they're NOT included, only every thing in between

|x|=8, x= 8 or -8

Answer 5

Dude, that just means that x={8,-8} but can't be lower than .5, which disproves -8, and can therefore just be a line at x=8.

Answer 6

it's probably a line at x=8

it's bigger than 0.5 and equals 8. =)