Absolute Value Equations Math Example 2

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Example 2

medium
Solve ∣2x+1∣=5|2x + 1| = 5.

Solution

  1. 1
    Case 1: 2x+1=5⇒2x=4⇒x=22x + 1 = 5 \Rightarrow 2x = 4 \Rightarrow x = 2.
  2. 2
    Case 2: 2x+1=−5⇒2x=−6⇒x=−32x + 1 = -5 \Rightarrow 2x = -6 \Rightarrow x = -3.
  3. 3
    Check: ∣2(2)+1∣=∣5∣=5|2(2)+1| = |5| = 5 ✓ and ∣2(−3)+1∣=∣−5∣=5|2(-3)+1| = |-5| = 5 ✓

Answer

x=2 or x=−3x = 2 \text{ or } x = -3
Isolate the absolute value first, then split into two cases. The two solutions are equidistant from x=−12x = -\frac{1}{2} (where the expression inside equals zero).

About Absolute Value Equations

Absolute value equations solve for values whose distance from zero or another number matches a target amount.

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Example 4 medium

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