Given that |4x – 2| = 10 and we need to find which value of x out of the option choices satisfies this.We can divide both the sides by 2 to get
\(\frac{|4x – 2|}{2} = \frac{10}{2}\)
=> |2x - 1| = 5
Let's understand how to solve this problem using two methods
Method 1: SubstitutionLet's take each answer choice and substitute in the question and check which one satisfies the question
A. −3 Put x = -3 in |2x - 1| = 5. We get
|2*(-3) - 1| = 5 => | -6 - 1| = |-7| = 7 \(\neq\) 5 => NOT POSSIBLE
B. −2 Put x = -2 in |2x - 1| = 5. We get
|2*(-2) - 1| = 5 => | -4 - 1| = |-5| = 5 = 5 => POSSIBLE
We don't need to solve further but solving to complete the problem
C. 1 Put x = 1 in |2x - 1| = 5. We get
|2*1 - 1| = 5 => | 2 - 1| = |1| = 1 \(\neq\) 5 => NOT POSSIBLE
D. 2 Put x = 2 in |2x - 1| = 5. We get
|2*2 - 1| = 5 => |4 - 1| = |3| = 3 \(\neq\) 5 => NOT POSSIBLE
E. 4 Put x = 4 in |2x - 1| = 5. We get
|2*4 - 1| = 5 => |8 - 1| = |7| = 7 \(\neq\) 5 => NOT POSSIBLE
Method 2: Algebra|2x - 1| = 5
Now, there are two ways of solving this
Method 2.1: SquaringSquare both the sides we get
\((|2x-1|)^2 = 5^2\)
=> \((2x-1) ^ 2 \)= 25
=> \((2x)^2 + 1^2 - 2*2x*1\) = 25
=> \(4x^2\) - 4x + 1 -25= 0
=> \(4x^2\) - 4x -24 = 0
Divide both sides by 4 we get
=> \(x^2\) - x - 6 =0
=> \(x^2\) -3x +2x - 6 =0
=> x*(x-3) 2*(x-3) = 0
=> (x-3) * (x+2) = 0
=> x = -2, 3
Method 2.2: Opening Absolute Value|2x - 1| = 5
=> 2x-1 = 5 or 2x-1 = -5
=> 2x = 5+1 = 2 or 2x = -5+1 = -4
=> 2x = 6 or 2x = -4
=> x = \(\frac{6}{2}\) = 3 or x = \(\frac{-4}{2}\)
=> x = 3 or x = -2
So,
Answer will be BHope it helps!
Watch the following video to learn the Basics of Absolute Values _________________