The solution set of the inequality is (- ∞, - 1].
What is the solution set of simultaneous inequality?
In this problem we have an inequality formed by two linear equations of the form f(x) ≥ g(x), whose solution set has to be found by using algebraic procedures:
- 1.5 · (4 · x + 1) ≥ 4.5 - 2.5 · (x + 1) Given
- 6 · x - 1.5 ≥ 4.5 - 2.5 · x - 2.5 Distributive property / (- 1) · a = - a / Definition of multiplication
- 3.5 ≥ 3.5 · x Compatibility with addition / Existence of the additive inverse / Modulative and associative properties / Definitions of addition and subtraction
- 1 ≥ x Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / - a / b = a / - b = - (a / b)
x ≤ - 1 Trichotomy / Result
The solution set of the inequality is (- ∞, - 1].
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