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Absolute Value Equations (Part 1) - Math, Class 11 Video Lecture - SSAT
FAQs on Absolute Value Equations (Part 1) - Math, Class 11
| 1. What is an absolute value equation? |  |
Ans. An absolute value equation is an equation that contains an absolute value expression. The absolute value of a number is its distance from zero on a number line. In an absolute value equation, the variable is inside the absolute value bars, and the equation is typically solved by considering both the positive and negative values that satisfy the equation.
| 2. How do you solve absolute value equations? | |
Ans. To solve an absolute value equation, you need to isolate the absolute value expression on one side of the equation. Then, you consider both the positive and negative cases by setting the expression equal to both the positive and negative value and solve for the variable in each case. The solutions are the values of the variable that make the equation true.
| 3. Can absolute value equations have more than one solution? | |
Ans. Yes, absolute value equations can have more than one solution. Since the absolute value of a number can be positive or negative, an absolute value equation can have two solutions, one for each case. However, there are also cases where the absolute value equation has only one solution or no solution at all.
| 4. What is the graphical representation of an absolute value equation? | |
Ans. The graphical representation of an absolute value equation is a V-shaped graph known as a "V-curve" or "V-shaped piecewise graph." The vertex of the V-curve represents the solution(s) of the equation. The curve opens upwards if the absolute value is positive and downwards if the absolute value is negative.
| 5. Can absolute value equations be applied in real-life situations? | |
Ans. Yes, absolute value equations have practical applications in real-life situations. For example, they can be used in physics to calculate distances, velocities, or accelerations. In finance, absolute value equations can be used to determine the absolute value of an investment's return or loss. Additionally, they can be applied in engineering, computer science, and many other fields where the concept of distance or magnitude is important.
Text Transcript from Video
We're told, solve the absolute
value of 3x minus 9 is equal
to 0, and graph the solution
on a number line.
So let's just rewrite the
absolute value equation.
They told us that the absolute
value of 3x minus
9 is equal to 0.
So we're told that the
absolute value of the
something-- in this case the
something is 3x minus 9-- is
equal to 0.
If I told you that the absolute
value of something is
equal to 0, I'm telling you
that something has to be
exactly 0 away from 0, or 0 away
from the origin on the
number line.
So the only thing that that
something could be is 0.
If I told you that the absolute
value of x is equal
to 0, you know that x has
to be equal to 0.
That's the only value whose
absolute value is 0.
So if I told you that the
absolute value of 3x minus 9
is 0, than we know that 3x minus
9 has to be equal to 0,
and that's kind of unique about
the 0 is that, it's the
only number the has a unique,
that's only the
absolute value of 0.
If you had, say, a 1 here, you
could say, oh well, then this
thing could be a 1
or a negative 1.
But here, if you have a 0,
this thing can only be 0.
So solving this equation is
fairly straightforward.
If we want to isolate the 3x,
get rid of the negative 9 on
the left-hand side, we add 9 to
both sides of the equation.
Add 9 to both sides
of the equation,
these 9's cancel out.
That's the whole point.
On the left-hand side, you're
just left with 3x, and on the
right-hand side, you are
just left with 9.
Now we want to solve for x,
so we have 3 times x.
Let's divide it by 3, because 3
times x divided by 3 is just
going to be x.
But if we divide the left side
by 3, we have to divide the
right side by 3.
So we are left with-- these
guys cancel out.
x is equal to 9 over
3, which is 3.
And that's our solution.
Now let's try out.
Let's make sure that this
actually works.
Let's substitute it back into
our original equation.
So we have the absolute
value of 3 times x.
Instead of x, I'll just put in
our actual answer that we got,
3 times 3 minus 9 has got
to be equal to 0.
So what's this going
to be equal to?
3 times 3 is 9.
So it's the absolute value of
9 minus 9, which is the
absolute value of 0, which
is, indeed, 0.
So it does, indeed, equal
0, and we are done.
value of 3x minus 9 is equal
to 0, and graph the solution
on a number line.
So let's just rewrite the
absolute value equation.
They told us that the absolute
value of 3x minus
9 is equal to 0.
So we're told that the
absolute value of the
something-- in this case the
something is 3x minus 9-- is
equal to 0.
If I told you that the absolute
value of something is
equal to 0, I'm telling you
that something has to be
exactly 0 away from 0, or 0 away
from the origin on the
number line.
So the only thing that that
something could be is 0.
If I told you that the absolute
value of x is equal
to 0, you know that x has
to be equal to 0.
That's the only value whose
absolute value is 0.
So if I told you that the
absolute value of 3x minus 9
is 0, than we know that 3x minus
9 has to be equal to 0,
and that's kind of unique about
the 0 is that, it's the
only number the has a unique,
that's only the
absolute value of 0.
If you had, say, a 1 here, you
could say, oh well, then this
thing could be a 1
or a negative 1.
But here, if you have a 0,
this thing can only be 0.
So solving this equation is
fairly straightforward.
If we want to isolate the 3x,
get rid of the negative 9 on
the left-hand side, we add 9 to
both sides of the equation.
Add 9 to both sides
of the equation,
these 9's cancel out.
That's the whole point.
On the left-hand side, you're
just left with 3x, and on the
right-hand side, you are
just left with 9.
Now we want to solve for x,
so we have 3 times x.
Let's divide it by 3, because 3
times x divided by 3 is just
going to be x.
But if we divide the left side
by 3, we have to divide the
right side by 3.
So we are left with-- these
guys cancel out.
x is equal to 9 over
3, which is 3.
And that's our solution.
Now let's try out.
Let's make sure that this
actually works.
Let's substitute it back into
our original equation.
So we have the absolute
value of 3 times x.
Instead of x, I'll just put in
our actual answer that we got,
3 times 3 minus 9 has got
to be equal to 0.
So what's this going
to be equal to?
3 times 3 is 9.
So it's the absolute value of
9 minus 9, which is the
absolute value of 0, which
is, indeed, 0.
So it does, indeed, equal
0, and we are done.
About this Video
Apr 19, 2026 Last updated
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