How do you solve the inequality $4.5 x - 3.8 \geq 1.5 x - 2.3$ $4.5x - 3.8 ≥ 1.5x - 2.3$ ?

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How do you solve the inequality $4.5 x - 3.8 \geq 1.5 x - 2.3$ $4.5x - 3.8 ≥ 1.5x - 2.3$ ?

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Answer 1 · 2016-01-03T10:57:07

$x \geq 0.5 = \frac{1}{2}$ $x>=0.5=1/2$

Explanation:

$4.5 x - 3.8 \geq 1.5 x - 2.3$ $4.5x-3.8>=1.5x-2.3$

Subtract $1.5 x$ $1.5x$ from both sides

$\Rightarrow 4.5 x - 3.8 - 1.5 x \geq 1.5 x - 2.3 - 1.5 x$ $implies 4.5x-3.8-1.5x>=1.5x-2.3-1.5x$
$\Rightarrow 3 x - 3.8 \geq - 2.3$ $implies 3x-3.8>=-2.3$

Add $3.8$ $3.8$ to both sides

$\Rightarrow 3 x - 3.8 + 3.8 \geq - 2.3 + 3.8$ $implies 3x-3.8+3.8>=-2.3+3.8$
$\Rightarrow 3 x \geq 1.5$ $implies 3x>=1.5$

Divide both sides by $3$ $3$

$\Rightarrow \frac{3 x}{3} \geq \frac{1.5}{3}$ $implies (3x)/3>=1.5/3$
$\Rightarrow x \geq 0.5 = \frac{1}{2}$ $implies x>=0.5=1/2$

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How do you solve the inequality $4.5 x - 3.8 \geq 1.5 x - 2.3$ $4.5x - 3.8 ≥ 1.5x - 2.3$ ?

1 Answer

Explanation:

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