|x - 1| = 6, quite hard.?

Question

Solve the following absolute value equation. Describe the graph as it would appear on a number line. Show your work. I did the work, but my teacher says its wrong. If you could please help me.

Answer 1

First part.... solve...
"Absolute value" is always greater than or equal to zero.
so |x - 1| = 6 means nothing more than
x - 1 = 6 (if x - 1 > 0 or x - 1 = 0) AND
x - 1 = -6 (if x - 1 < 0)
Solve both.

Second part... describe the graph...
The graph would be the solution set for y = x - 1 (if x - 1 is greater than zero) and y = -(x - 1) (if x - 1 is less than zero).
But the equation states that y is always equal to 6 or -6
What does the graph of y = 6 look like? Think... for whatever value you give x (as long as it's greater than or equal to 1), y is always 6... plot a few points.... x = 1, y = 6... x = 2, y = 6.... x = 3, y = 6...x = 5, y = 6... get the picture? That's half of the graph...'
The other half is where x - 1 < 0... x = 0, y = -6,... x = -3, y = -6...

Now... all you have to know is how to graph a line that excludes a point. -----------o where the o indicates the point that's excluded. It means that the line goes all the way up to that point, but doesn't exist at that point. Without that notation, the graph would indicate that the point was included.

Don't argue with the teacher... but the "number line" is usually depicted as horizontal... and therefore the X axis. So, in fact, the graph is not "ON the number line," but above and below it in what you will probably someday call the Cartesian coordinates or the Cartesian plane or maybe even "two-space". ;-)

Answer 2

If |x-1| = 6 then
x-1 = 6 or x-1 = -6 so
x = 7 or x = -5

Answer 3

|x - 1| = 6

This splits into two equations by definition of absolute value.

x - 1 = 6
x - 1 = -6

Solve each equation, and that gives you your solutions. From the first equation, x = 7. From the second equation, x = -5.
Therefore, your answers are x = {7, -5}

On a number line, the 1 would be your "center". The 6 represents the distance both ways (left and right) from 1.

Answer 4

with an absolute value all values will be positive, so you will have 2 solutions

first we can simply add 1 to each side and solve for x getting one solution
x -1 +1 = 6+1
x=7
ok now we figure out what value of x will get us a -6? Well lets just solve for it like we did before
x-1 = -6
add one to each side
x -1 +1 =-6 +1
x = -5
so your solutions are x=-5 & 7

Answer 5

hi x* a million/5 - a million/6 = 30 x*a million/5 = 30+a million/6 ......you probably did it suitable you could write 30 as (30*6)/6 , can not you? x*a million/5 = (30*6)/6 + a million/6 .....wow we've a similar denominator x*a million/5 = (30*6+a million)/6 = (one hundred eighty+a million)/6= 181/6 multiply the two aspects by 5 .....crossing works 5*x*a million/5= 181/6 *5 x= (181*5)/6 = 905/6 wish this is finished by a thank you to income greater qualifications by training

Answer 6

x=7 & -5.
graf of |x-1|=1-x between - infinity, 1,
and x-1 between 1 and infinity,
you should not have negative value o graf

Answer 7

so X-1 could be 6 so then X = 7
X-1 could be -6 so... X=-5
the graph is .. 2 points: one at (-5,0) and one at (7,0)

Answer 8

∣x - 1∣= 6

x - 1 = 6

x - 1 + 1 = 6 + 1

x = 7

- - - - - - - - -s-

Answer 9

u dont no this? dude, the x is the missing numba now if SOMETHING minus 1 = 6, what is the missing numba?

obvious, dont u think?

by the way, its 7
lol im such a nerd

Answer 10

x = pos or neg 7. closed points on pos and neg 7