x > 8 or x < -2/5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtract Property of Equality
Algebra I
Solving inequalities|Absolute Values| - makes any negative number positive
Step-by-step explanation:
Step 1: Define
|2x + 5| < 3|x - 1|
Step 2: Rewrite
When solving for absolute values, x can be ± since the absolute value makes all values positive.
Positive x equation: |2x + 5| < 3|x - 1|
Negative x equation: |2x + 5| < -3|x - 1|
Step 3: Solve for x
When solving, we can replace the absolute value with parenthesis because we have now rewritten the absolute value in dual form.
2x + 5 < 3(x - 1)
2x + 5 < -3(x - 1)
Positive Equation
[Division Property of Equality] Divide both sides by 3:
[Addition Property of Equality] Add 1 on both sides:
[Subtraction Property of Equality] Isolate x terms:
[Multiplication Property of Equality] Multiply 3 on both sides:
Negative Equation
[Division Property of Equality] Divide both sides by -3:
[Addition Property of Equality] Add 1 on both sides:
[Addition Property of Equality] Isolate x terms:
[Division Property of Equality] Isolate x term:
We see that our inequality values are x < -2/5 and/or x > 8.
∴ We have solved your absolute value inequality problem.
Hope this helps! <3 :)