An algebra problem by bhakti dongerkery

Algebra Level 2

Solve the inequality 1 2 x + 3 < 2 x − 6 \dfrac{1}{2}x + 3 < 2x - 6 for x x .

x < 6 x < 6 x < − 6 5 x < -\frac65 x > 6 x > 6 x > − 5 6 x > -\frac56

Bhakti Dongerkery by bhakti dongerkery , 19, USA

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3 solutions

Mahdi Raza
Jun 8, 2020

1 2 x + 3 < 2 x − 6 x + 6 < 4 x − 12 Multiply by 2 − 3 x < − 18 3 x > 18 Sign Changes \begin{aligned} \dfrac{1}{2}x + 3 &< 2x - 6 \\ x + 6 &< 4x - 12 &\color{#3D99F6}{\text{Multiply by 2}} \\ -3x&<-18 \\ 3x&>18 &\color{#3D99F6}{\text{Sign Changes}} \end{aligned}

x > 6 \boxed{x>6}

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x 2 + 3 < 2 x − 6 \dfrac{x}{2} + 3 < 2x - 6

\(\dfrac{3x}{2} > 9

\)

3 x > 18 3x > 18

x > 6 \boxed{x > 6}

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Sagar Shah
Nov 21, 2015

We have,

x/2 + 3 < 2x - 6

=> 6 + 3 < 2x - x/2

=> 9 < 3x/2

=> 18 < 3x

=> 6 < x or x > 6.

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