Question

What value ofx is in the solution set of 3(x-4)>5x +2?

Answer 1

$\boldsymbol{\sf{3(x-4) > 5x +2 }}$

Use the distributive property to multiply 3 by x−4.

$\boldsymbol{\sf{3x-12 > 5x+2 }}$

Subtract 5x on both sides.

$\boldsymbol{\sf{3x-12-5x > 2 } }$

Combine 3x and −5x to get −2x.

$\boldsymbol{\sf{-2x-12 > 2 }}$

Add 12 to both sides.

$\boldsymbol{\sf{-2x > 2+12 \ \longmapsto \ \ [Add \ 2 +12]}}$

$\boldsymbol{\sf{-2x > 14}}$

Divide both sides by −2. Since −2 is < 0, the inequality direction is changed.

$\boldsymbol{\sf{x < \dfrac{14}{-2} \ \ \longmapsto \ \ \ [Split]}}$

$\boxed{\boldsymbol{\sf{x < -7 }}}$

So in the inequality 3(x-4)>5x +2, the value of x is -7.

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