Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De vergelijking $https://latex.codecogs.com/png.image?\large \dpi{110}4-\sqrt{2}\: x<5-x$ 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)-3.11.2023 ]

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. $\boldsymbol{x>-\,\frac {\sqrt2\,+\,1} {3} }$
	D. $\boldsymbol{x< \sqrt2 + 1}$
	E. $\boldsymbol{x < -1-\sqrt2}$
	F. $\boldsymbol{x > -1-\sqrt2}$

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}4-\sqrt2x<5-x\\\Leftrightarrow \; x-\sqrt2x<5-4\\\Leftrightarrow \;(1-\sqrt2)x<1\\\Leftrightarrow \;x>\frac{1}{1-\sqrt2}\\\Leftrightarrow \;x>\frac{1+\sqrt2}{(1-\sqrt2)(1+\sqrt2)}\\\Leftrightarrow \;x>\frac{1+\sqrt2}{1-2}\\\Leftrightarrow \;x>-(1+\sqrt2)\\\Leftrightarrow \;x>-1-\sqrt2\\$

De vergelijking $https://latex.codecogs.com/png.image?\large \dpi{110}4-\sqrt{2}\: x<5-x$ 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. \(\boldsymbol{x>-\,\frac {\sqrt2\,+\,1} {3} }\)
	D. \(\boldsymbol{x< \sqrt2 + 1}\)
	E. \(\boldsymbol{x < -1-\sqrt2}\)
	F. \(\boldsymbol{x > -1-\sqrt2}\)