a)	\displaystyle \displaystyle\frac{5x}{6}-\displaystyle\frac{x+2}{9}=\displaystyle\frac{1}{2}	b)	\displaystyle \displaystyle\frac{8x+3}{7}-\displaystyle\frac{5x-7}{4}=2
c)	\displaystyle (x+3)^2-(x-5)^2=6x+4	d)	\displaystyle (x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2

Antwort

Antwort 2.2:2

Lösung a

Lösung 2.2:2a

Lösung b

Lösung 2.2:2b

Lösung c

Lösung 2.2:2c

Lösung d

Lösung 2.2:2d

Übung 2.2:3

Solve the equations

a)	\displaystyle \displaystyle\frac{x+3}{x-3}-\displaystyle\frac{x+5}{x-2}=0
b)	\displaystyle \displaystyle\frac{4x}{4x-7}-\displaystyle\frac{1}{2x-3}=1
c)	\displaystyle \left(\displaystyle\frac{1}{x-1}-\frac{1}{x+1}\right)\left(x^2+\frac{1}{2}\right)=\displaystyle\frac{6x-1}{3x-3}
d)	\displaystyle \left(\displaystyle\frac{2}{x}-3\right)\left(\displaystyle\frac{1}{4x}+\frac{1}{2}\right)-\left(\displaystyle\frac{1}{2x}-\frac{2}{3}\right)^2-\left(\displaystyle\frac{1}{2x}+\frac{1}{3}\right)\left(\displaystyle\frac{1}{2x}-\frac{1}{3}\right)=0

Antwort

Lösung a

Lösung b

Lösung c

Lösung d

Übung 2.2:4

a)	Write the equation for the line \displaystyle \,y=2x+3\, in the form \displaystyle \,ax+by=c\,.
b)	Write the equation for the line \displaystyle 3x+4y-5=0 in the form \displaystyle \,y=kx+m\,.

Antwort

Antwort 2.2:4

Lösung a

Lösung 2.2:4a

Lösung b

Lösung 2.2:4b

Übung 2.2:5

a)	Determine the equation for the straight line that goes between the points \displaystyle \,(2,3)\, and\displaystyle \,(3,0)\,.
b)	Determine the equation for the straight line that has slope \displaystyle \,-3\, and goes through the point \displaystyle \,(1,-2)\,.
c)	Determine the equation for the straight line that goes through the point \displaystyle \,(-1,2)\, and is parallel to the line \displaystyle \,y=3x+1\,.
d)	Determine the equation for the straight line that goes through the point \displaystyle \,(2,4)\, and is perpendicular to the line \displaystyle \,y=2x+5\,.
e)	Determine the slope, \displaystyle \,k\,, for the straight line that cuts the x-axis at the point \displaystyle \,(5,0)\, and y-axis at the point \displaystyle \,(0,-8)\,.

Antwort

Lösung a

Lösung b

Lösung c

Lösung d

Lösung e

Übung 2.2:6

Find the points of intersection between the pairs of lines in the following

a)	\displaystyle y=3x+5\ and the x-axis	b)	\displaystyle y=-x+5\ and the y-axis
c)	\displaystyle 4x+5y+6=0\ and the y-axis	d)	\displaystyle x+y+1=0\ and \displaystyle \ x=12
e)	\displaystyle 2x+y-1=0\ and \displaystyle \ y-2x-2=0

Antwort

Lösung a

Lösung b

Lösung c

Lösung d

Lösung e

Übung 2.2:7

Sketch the graph of the functions

\displaystyle f(x)=3x-2

\displaystyle f(x)=2-x

\displaystyle f(x)=2

Antwort

Lösung a

Lösung b

Lösung c

Übung 2.2:8

In the xy-plane, fill in all the points whose coordinates \displaystyle \,(x,y)\, satisfy

\displaystyle y \geq x

\displaystyle y < 3x -4

\displaystyle 2x+3y \leq 6

Antwort

Lösung a

Lösung b

Lösung c

Übung 2.2:9

Calculate the area of the triangle which

a)	has corners at the points \displaystyle \,(1,4)\,, \displaystyle \,(3,3)\, and \displaystyle \,(1,0)\,.
b)	is bordered by the lines \displaystyle \ x=2y\,, \displaystyle \ y=4\ and \displaystyle \ y=10-2x\,.
c)	is described by the inequalities \displaystyle \ x+y \geq -2\,, \displaystyle \ 2x-y \leq 2\ and \displaystyle \ 2y-x \leq 2\,.