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2.2 Exercises

From Förberedande kurs i matematik 1

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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
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| style="border-bottom:1px solid #000" width="5px" |  
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{{Ej vald flik|[[2.2 Linjära uttryck|Theory]]}}
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{{Not selected tab|[[2.2 Linear expressions|Theory]]}}
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{{Vald flik|[[2.2 Övningar|Exercises]]}}
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{{Selected tab|[[2.2 Exercises|Exercises]]}}
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|| <math>5x+7=2x-6</math>
|| <math>5x+7=2x-6</math>
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</div>{{#NAVCONTENT:Answer|Svar 2.2:1|Solution a|Lösning 2.2:1a|Solution b|Lösning 2.2:1b|Solution c|Lösning 2.2:1c|Solution d|Lösning 2.2:1d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:1|Solution a|Solution 2.2:1a|Solution b|Solution 2.2:1b|Solution c|Solution 2.2:1c|Solution d|Solution 2.2:1d}}
===Exercise 2.2:2===
===Exercise 2.2:2===
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|| <math>(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2</math>
|| <math>(x^2+4x+1)^2+3x^4-2x^2=(2x^2+2x+3)^2</math>
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:2|Solution a|Lösning 2.2:2a|Solution b|Lösning 2.2:2b|Solution c|Lösning 2.2:2c|Solution d|Lösning 2.2:2d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:2|Solution a|Solution 2.2:2a|Solution b|Solution 2.2:2b|Solution c|Solution 2.2:2c|Solution d|Solution 2.2:2d}}
===Exercise 2.2:3===
===Exercise 2.2:3===
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|| <math>\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</math>
|| <math>\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</math>
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:3|Solution a|Lösning 2.2:3a|Solution b|Lösning 2.2:3b|Solution c|Lösning 2.2:3c|Solution d|Lösning 2.2:3d}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:3|Solution a|Solution 2.2:3a|Solution b|Solution 2.2:3b|Solution c|Solution 2.2:3c|Solution d|Solution 2.2:3d}}
===Exercise 2.2:4===
===Exercise 2.2:4===
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|| Write the equation for the line <math> 3x+4y-5=0</math> in the form <math>\,y=kx+m\,</math>.
|| Write the equation for the line <math> 3x+4y-5=0</math> in the form <math>\,y=kx+m\,</math>.
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:4|Solution a|Lösning 2.2:4a|Solution b|Lösning 2.2:4b}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:4|Solution a|Solution 2.2:4a|Solution b|Solution 2.2:4b}}
===Exercise 2.2:5===
===Exercise 2.2:5===
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|| Determine the slope, <math>\,k\,</math>, for the straight line that cuts the ''x''-axis at the point <math>\,(5,0)\,</math> and ''y''-axis at the point <math>\,(0,-8)\,</math>.
|| Determine the slope, <math>\,k\,</math>, for the straight line that cuts the ''x''-axis at the point <math>\,(5,0)\,</math> and ''y''-axis at the point <math>\,(0,-8)\,</math>.
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:5|Solution a|Lösning 2.2:5a|Solution b|Lösning 2.2:5b|Solution c|Lösning 2.2:5c|Solution d|Lösning 2.2:5d|Solution e|Lösning 2.2:5e}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:5|Solution a|Solution 2.2:5a|Solution b|Solution 2.2:5b|Solution c|Solution 2.2:5c|Solution d|Solution 2.2:5d|Solution e|Solution 2.2:5e}}
===Exercise 2.2:6===
===Exercise 2.2:6===
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{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="50%" | <math>y=3x+5\ </math> and ''x''-axeln
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|width="50%" | <math>y=3x+5\ </math> and the ''x''-axis
|b)
|b)
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|width="50%" | <math>y=-x+5\ </math> and ''y''-axeln
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|width="50%" | <math>y=-x+5\ </math> and the ''y''-axis
|-
|-
|c)
|c)
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|width="50%" | <math>4x+5y+6=0\ </math> and ''y''-axeln
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|width="50%" | <math>4x+5y+6=0\ </math> and the ''y''-axis
|d)
|d)
|| <math>x+y+1=0\ </math> and <math>\ x=12</math>
|| <math>x+y+1=0\ </math> and <math>\ x=12</math>
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|| <math>2x+y-1=0\ </math> and <math>\ y-2x-2=0</math>
|| <math>2x+y-1=0\ </math> and <math>\ y-2x-2=0</math>
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:6|Solution a|Lösning 2.2:6a|Solution b|Lösning 2.2:6b|Solution c|Lösning 2.2:6c|Solution d|Lösning 2.2:6d|Solution e|Lösning 2.2:6e}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:6|Solution a|Solution 2.2:6a|Solution b|Solution 2.2:6b|Solution c|Solution 2.2:6c|Solution d|Solution 2.2:6d|Solution e|Solution 2.2:6e}}
===Exercise 2.2:7===
===Exercise 2.2:7===
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|width="33%" | <math>f(x)=2</math>
|width="33%" | <math>f(x)=2</math>
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:7|Solution a|Lösning 2.2:7a|Solution b|Lösning 2.2:7b|Solution c|Lösning 2.2:7c}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:7|Solution a|Solution 2.2:7a|Solution b|Solution 2.2:7b|Solution c|Solution 2.2:7c}}
===Exercise 2.2:8===
===Exercise 2.2:8===
<div class="ovning">
<div class="ovning">
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In the ''xy''-plane, fill in all the points whose coordinates <math>\,(x,y)\,</math> satisfy
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In the ''xy''-plane, shade in the section whose coordinates <math>\,(x,y)\,</math> satisfy
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="33%" | <math>2x+3y \leq 6 </math>
|width="33%" | <math>2x+3y \leq 6 </math>
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:8|Solution a|Lösning 2.2:8a|Solution b|Lösning 2.2:8b|Solution c|Lösning 2.2:8c}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:8|Solution a|Solution 2.2:8a|Solution b|Solution 2.2:8b|Solution c|Solution 2.2:8c}}
===Exercise 2.2:9===
===Exercise 2.2:9===
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|| is described by the inequalities <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> and <math>\ 2y-x \leq 2\,</math>.
|| is described by the inequalities <math>\ x+y \geq -2\,</math>, <math>\ 2x-y \leq 2\ </math> and <math>\ 2y-x \leq 2\,</math>.
|}
|}
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</div>{{#NAVCONTENT:Answer|Svar 2.2:9|Solution a|Lösning 2.2:9a|Solution b|Lösning 2.2:9b|Solution c|Lösning 2.2:9c}}
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</div>{{#NAVCONTENT:Answer|Answer 2.2:9|Solution a|Solution 2.2:9a|Solution b|Solution 2.2:9b|Solution c|Solution 2.2:9c}}

Current revision

       Theory          Exercises      

Exercise 2.2:1

Solve the equations

a) x−2=−1 b) 2x+1=13
c) 31x−1=x d) 5x+7=2x−6

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.2:2

Solve the equations

a) 65x−9x+2=21 b) 78x+3−45x−7=2
c) (x+3)2−(x−5)2=6x+4 d) (x2+4x+1)2+3x4−2x2=(2x2+2x+3)2

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.2:3

Solve the equations

a) x−3x+3−x−2x+5=0
b) 4x4x−7−12x−3=1
c) 1x−1−1x+1x2+21=3x−36x−1 
d) x2−314x+21−12x−322−12x+3112x−31=0 

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 2.2:4

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

Answer | Solution a | Solution b

Exercise 2.2:5

a) Determine the equation for the straight line that goes between the points (23) and(30).
b) Determine the equation for the straight line that has slope −3 and goes through the point (1−2).
c) Determine the equation for the straight line that goes through the point (−12) and is parallel to the line y=3x+1.
d) Determine the equation for the straight line that goes through the point (24) and is perpendicular to the line y=2x+5.
e) Determine the slope, k, for the straight line that cuts the x-axis at the point (50) and y-axis at the point (0−8).

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 2.2:6

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

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

Answer | Solution a | Solution b | Solution c | Solution d | Solution e

Exercise 2.2:7

Sketch the graph of the functions

a) \displaystyle f(x)=3x-2 b) \displaystyle f(x)=2-x c) \displaystyle f(x)=2

Answer | Solution a | Solution b | Solution c

Exercise 2.2:8

In the xy-plane, shade in the section whose coordinates \displaystyle \,(x,y)\, satisfy

a) \displaystyle y \geq x b) \displaystyle y < 3x -4 c) \displaystyle 2x+3y \leq 6

Answer | Solution a | Solution b | Solution c

Exercise 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\,.

Answer | Solution a | Solution b | Solution c

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