Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De vergelijking $4-\sqrt{2}\: x<5-x$ is gelijkwaardig met	A. $\boldsymbol{x>\sqrt2 - 1 }$
	B. $\boldsymbol{x>1-\sqrt2 }$
	C. $\boldsymbol{x>-\,\frac{\sqrt 2\,+\,1} {3} }$
	D. $\boldsymbol{x < \sqrt2 + 1 }$
	E. $\boldsymbol{x < -1-\sqrt2 }$
	F. $\boldsymbol{x > -1-\sqrt2 }$

[ 4-4893 - op net sinds 23.10.06-(E)-17.11.2024 ]

Translation in E N G L I S H

The equation $4-\sqrt{2}\: x<5-x$ is equivalent with	A. $\boldsymbol{x>\sqrt2 - 1 }$
	B. $\boldsymbol{x>1-\sqrt2 }$
	C. $\boldsymbol{x>-\,\frac{\sqrt 2\,+\,1} {3} }$
	D. $\boldsymbol{x < \sqrt2 + 1 }$
	E. $\boldsymbol{x < -1-\sqrt2 }$
	F. $\boldsymbol{x > -1-\sqrt2 }$

Oplossing - Solution

$\begin{aligned}4-\sqrt2x<5-x\\\Leftrightarrow\;x-\sqrt2x<5-4\\\Leftrightarrow\;(1-\sqrt2)x<1\\\Leftrightarrow\;x>\frac{1}{1-\sqrt2}\\\Leftrightarrow\;x>\frac{1+\sqrt2}{(1-\sqrt2)(1+\sqrt2)}\\\Leftrightarrow\;x>\frac{1+\sqrt2}{1-2}\\\Leftrightarrow\;x>-(1+\sqrt2)\\\Leftrightarrow\;x>-1-\sqrt2\end{aligned}$

De vergelijking $4-\sqrt{2}\: x<5-x$ is gelijkwaardig met	A. \(\boldsymbol{x>\sqrt2 - 1 }\)
	B. \(\boldsymbol{x>1-\sqrt2 }\)
	C. \(\boldsymbol{x>-\,\frac{\sqrt 2\,+\,1} {3} }\)
	D. \(\boldsymbol{x < \sqrt2 + 1 }\)
	E. \(\boldsymbol{x < -1-\sqrt2 }\)
	F. \(\boldsymbol{x > -1-\sqrt2 }\)

The equation $4-\sqrt{2}\: x<5-x$ is equivalent with	A. \(\boldsymbol{x>\sqrt2 - 1 }\)
	B. \(\boldsymbol{x>1-\sqrt2 }\)
	C. \(\boldsymbol{x>-\,\frac{\sqrt 2\,+\,1} {3} }\)
	D. \(\boldsymbol{x < \sqrt2 + 1 }\)
	E. \(\boldsymbol{x < -1-\sqrt2 }\)
	F. \(\boldsymbol{x > -1-\sqrt2 }\)