Question

Classify: −4m+21(m−1)≤15m+2(m−1).

Answer 1

Answer:

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

Step-by-step 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:

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

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

$\sf 2(m-1)$

$\hookrightarrow 2m-2$

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

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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