Question

Classify: −4m+21(m−1)≤15m+2(m−1).

Answer 1

`\boxed{\sf All\: real\: numbers}`

Explanation:

`\star \:\sf Classify\: -4m+21\left(m-1\right)\le \:15m+2\left(m-1\right)\: \star`

Apply Distribution law:

`\sf -4m+21m-21\le \:15m+2\left(m-1\right)`

Combine like terms:

**
`\sf \hookrightarrow -4m+21m=17m`

`\longmapsto\sf 17m-21\le \:15m+2\left(m-1\right)`

`\sf 2(m-1)`

`\hookrightarrow 2m-2`

-----------------------------------------

`\longmapsto\sf 17m-21\le \:15m+2m-2`

Combine like terms:

**
`\sf 15m+2m=17m`

`\longmapsto\sf 17m-21\le \:17m-2`

Add 21 from both sides:

`\longmapsto\sf 17m-21+21\le \:17m-2+21`

`\longmapsto\sf 17m\le \:17m+19`

Subtract 17m from both sides:

`\longmapsto\sf 17m-17m\le \:17m+19-17m`

`\longmapsto\sf 0\le \:19`

Therefore, the solution of the inequality: All real numbers

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