The solution set for inequation 3(7 − x) $\geq$ 15 − 7x (x+1)/3, x ∈ R is ______.

Question

The solution set for inequation 3(7 − x) $\geq$ 15 − 7x > (x+1)/3, x ∈ R is ______.

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The solution set for inequation 3(7 − x) $\geq$ 15 − 7x > (x+1)/3, x ∈ R is \underline(-$\frac{3}{2}$ <= x < 2). Explanation: 3(7 − x) $\geq$ 15 − 7x > (x+1)/3 3(7 − x) $\geq$ 15 − 7x $\Rightarrow$ 21 − 3x $\geq$ 15 − 7x $\Rightarrow$ 4x $\geq$ −6 $\Rightarrow$ x $\geq$ −$\frac{3}{2}$ 15 − 7x > (x+1)/3 $\Rightarrow$ 45 − 21x > x + 1 $\Rightarrow$ −22x > −44 $\Rightarrow$ x < 2 Combine: −$\frac{3}{2}$ $\leq$ x < 2

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