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In this video, I’ll show you two quick and easy methods to solve the absolute value equation |x-2| = |x+5| . Whether you’re a student brushing up on your math skills or just looking for a simple solution, this step-by-step guide will walk you through both a geometric interpretation and an algebraic approach.
#maths #mathematics #equation #mathproblems #absolutevalue
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0:00
hello welcome to we learn
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daily in this video we're going to solve
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the equation where the absolute value of
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the difference between X and 2 equals
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the absolute value of the sum of X and 5
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as usual before watching try to solve
0:17
this equation on your own let's start
0:20
we'll solve this equation using two
0:22
methods the first method is based on the
0:24
geometric meaning of absolute value
0:28
specifically we need to remember that
0:30
the absolute value of the difference
0:32
between two numbers A and B represents
0:36
the distance between points A and B on
0:38
the number line regardless of which
0:40
number is larger to use the geometric
0:43
meaning of absolute value we need to
0:45
express each absolute value expression
0:48
as a difference this means we leave the
0:50
first absolute value as it is the
0:52
absolute value of x - 2 and rewrite the
0:55
second absolute value the absolute value
0:58
of x + 5 as the absolute value of x -
1:02
-5 now the left side represents the
1:05
distance from point x to 2 and the right
1:08
side represents the distance from point
1:09
x to -5 these distances must be equal
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which means the point x must be
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equidistant from -5 and 2 this condition
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can only be true if the point x
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coincides with the midpoint of the
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segment from -5 to
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2 so we can find the value of x by
1:28
calculating the arithmetic mean of of -5
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and
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2 adding -5 and 2 then dividing by two
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gives us -3 halves or in decimal form -
1:39
1 and a half now for the second
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method since absolute value is always
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non- negative we conclude that both the
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left and right sides of the equation are
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greater than or equal to zero this
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allows us to square both sides of the
1:55
equation without changing the solution
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so we can replace the the original
2:00
equation with the equality of the
2:02
squares of these absolute values this
2:04
means the square of the first absolute
2:07
value x - 2 must equal the square of the
2:11
second absolute value x + 5 we recall
2:15
that the square of an absolute value is
2:17
equal to the square of the expression
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inside the absolute value this allows us
2:22
to replace the absolute value signs with
2:25
regular parentheses giving us a simpler
2:27
equation the square of x - 2 = x + 5
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next we move everything to one side of
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the equation resulting in the difference
2:37
of squares the square of x - 2 - the
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square of x + 5 =
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0 using the difference of squares
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formula the left side can be factored
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into x - 2 - x - 5 multiplied x - 2 + x
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+ 5 simplifying the Expressions inside
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the parentheses the first Factor becomes
3:00
-7 and the second Factor becomes 2 * x +
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3 setting the product equal to 0 we
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divide both sides by -7 leaving us with
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2 * x + 3 = 0 solving for x we get 2 * x
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= -3 which simplifies to x = -3 or - 1
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and A2 finally we write the answer x =
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-1 A2 the problem is solved
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if you found the solution helpful please
3:32
like the video subscribe and leave a
3:34
comment thank you for watching goodbye
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