See the entire solution process below:
First, divide each side of the equation by #color(red)(4)# to isolate the absolute value term while keeping the equation balanced:
#(4abs(0.5x - 2.5))/color(red)(4) = 0/color(red)(4)#
#(color(red)(cancel(color(black)(4)))abs(0.5x - 2.5))/cancel(color(red)(4)) = 0#
#abs(0.5x - 2.5) = 0#
The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. However, because #0# has no positive or negative form we just need to solve:
#0.5x - 2.5 = 0#
Now, add #color(red)(2.5)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#0.5x - 2.5 + color(red)(2.5) = 0 + color(red)(2.5)#
#0.5x - 0 = 2.5#
#0.5x = 2.5#
Now, divide each side of the equation by #color(red)(0.5)# to solve for #x# while keeping the equation balanced:
#(0.5x)/color(red)(0.5) = 2.5/color(red)(0.5)#
#(color(red)(cancel(color(black)(0.5)))x)/cancel(color(red)(0.5)) = 5#
#x = 5#
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Find All Complex Solutions 4|0.5x-2.5|=0
Step 1
Factor out of .
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Factor out of .
Factor out of .
Factor out of .
Step 2
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Apply the distributive property.
Multiply by .
Simplify the right side.
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Divide by .
Step 3
Remove the absolute value term. This creates a on the right side of the equation because .
Step 4
Plus or minus is .
Step 5
Add to both sides of the equation.
Step 6
Divide each term in by and simplify.
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Divide each term in by .
Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify the right side.
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Divide by .
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What is the solution to 4|0.5x – 2.5| = 0?
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1
What is the solution to 4|0.5x – 2.5| = 0?
Guest May 7, 2017
0 users composing answers..
1+0 Answers
#1
+1
Solve for x over the real numbers:
4 abs(0.5 x - 2.5) = 0
4 abs(0.5 x - 2.5) = 4 abs(x/2 - 5/2):
4 abs(x/2 - 5/2) = 0
Divide both sides by 4:
abs(x/2 - 5/2) = 0
Eliminate the absolute value:
1 (x/2 - 5/2) = 0
Divide both sides by 1:
x/2 - 5/2 = 0
Bring x/2 - 5/2 together using the
common denominator 2:
(x - 5)/2 = 0
Multiply both sides by 2:
x - 5 = 0
Add 5 to both sides:
Answer: | x = 5
Guest May 7, 2017
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