LINR 2 | Lesson 2 | Practice (Solving Inequalities Solutions)

1.  \(\frac{2}{3}x- 1\geq11\) \[\frac{2}{3}x- 1\geq11\]\[\frac{2}{3}x- 1+1\geq11+1\]\[\frac{2}{3}x\geq12\]\[\frac{3}{2}\bigg(\frac{2}{3}x\bigg)\geq12\bigg(\frac{3}{2}\bigg)\]\[x ≥18\]


2.  \(2(x-1)\geq 3-2x\)\[2(x-1)\geq 3-2x\]\[2x-2\geq 3-2x\]\[2x+2x-2\geq 3-2x+2x\]\[4x-2\geq 3\]\[4x-2+2)\geq 3+2\]\[4x ≥ 5\]\[x ≥ \frac{5}{4}\]


3. \(4(3x-2) ≤ 5(3x+2)\)\[4(3x-2) ≤ 5(3x+2)\]\[12x-8 ≤ 15x+10\]\[12x-15x-8 ≤ 15x-15x+10\]\[-3x-8 ≤ 10\]\[-3x-8+8 ≤ 10+8\]\[-3x ≤ 18\]\[\frac{-3x}{-3} ≤ \frac{18}{-3}\]\[x ≥ -6\]


4.  \(500 + 0.03x ≥ 740\) \[500 + 0.03x ≥ 740\]\[500-500 + 0.03x ≥ 740-500\]\[ 0.03x ≥ 240\]\[ \frac{0.03}{0.03} ≥ \frac{240}{0.03}\]\[x≥8000\]

The sales person would need to sell at least $8000 to earn at least $740.


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