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

1.  \(\dfrac{2}{3}x- 1\geq11\)

\[\begin{align}\dfrac{2}{3}x-1&\geq11\\\\\dfrac{2}{3}x-1+1&\geq11+1\\\\\dfrac{2}{3}x&\geq12\\\\\dfrac{3}{2}\bigg(\dfrac{2}{3}x\bigg)&\geq12\bigg(\dfrac{3}{2}\bigg)\\\\x &\geq18\end{align}\]


2.  \(2(x-1)\geq 3-2x\)

\[\begin{align}2(x-1)&\geq 3-2x\\\\2x-2&\geq 3-2x\\\\2x+2x-2&\geq 3-2x+2x\\\\4x-2&\geq 3\\\\4x-2+2&\geq 3+2\\\\4x &\geq 5\\\\x &\geq \dfrac{5}{4}\end{align}\]


3. \(4(3x-2) ≤ 5(3x+2)\)

\[\begin{align}4(3x-2) &≤ 5(3x+2)\\\\12x-8 &≤ 15x+10\\\\12x-15x-8 &≤ 15x-15x+10\\\\-3x-8 &≤ 10\\\\-3x-8+8 &≤ 10+8\\\\-3x &≤ 18\\\\\dfrac{-3x}{-3} &≤ \dfrac{18}{-3}\\\\x &≥ -6\end{align}\]


4.  \(500 + 0.03x ≥ 740\)

\[\begin{align}500 + 0.03x &≥ 740\\\\500-500 + 0.03x &≥ 740-500\\\\ 0.03x &≥ 240\\\\ \dfrac{0.03}{0.03} &≥ \dfrac{240}{0.03}\\\\x &≥8000\end{align}\]

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


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