Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(5(5x-\frac{2}{9})=2x+\frac{9}{2}\)
2. \(7(-4x-\frac{3}{5})=2x+\frac{8}{11}\)
3. \(-6(5x+\frac{2}{5})=-7x+\frac{10}{9}\)
4. \(-3(4x-\frac{5}{4})=-5x+\frac{6}{5}\)
5. \(3(-3x-\frac{3}{11})=-5x+\frac{4}{5}\)
6. \(6(-2x+\frac{3}{11})=-5x+\frac{4}{7}\)
7. \(3(3x+\frac{2}{11})=2x+\frac{2}{9}\)
8. \(6(3x+\frac{5}{7})=-7x+\frac{4}{3}\)
9. \(5(5x+\frac{4}{9})=-7x+\frac{6}{11}\)
10. \(3(-2x-\frac{3}{2})=-7x+\frac{10}{7}\)
11. \(4(4x-\frac{2}{3})=3x+\frac{10}{9}\)
12. \(-5(-4x-\frac{2}{7})=3x+\frac{8}{5}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{9})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 25x-\frac{10}{9}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{450}{ \color{blue}{18} }x- \frac{20}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 450x \color{red}{-20} & = & \color{red}{36x} +81 \\\Leftrightarrow & 450x \color{red}{-20} \color{blue}{+20} \color{blue}{-36x} & = & \color{red}{36x} +81 \color{blue}{-36x} \color{blue}{+20} \\\Leftrightarrow & 450x-36x& = & 81+20 \\\Leftrightarrow & \color{red}{414} x& = & 101 \\\Leftrightarrow & x = \frac{101}{414} & & \\ & V = \left\{ \frac{101}{414} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{5})& = & 2x+\frac{8}{11} \\\Leftrightarrow & -28x-\frac{21}{5}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{231}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-231} & = & \color{red}{110x} +40 \\\Leftrightarrow & -1540x \color{red}{-231} \color{blue}{+231} \color{blue}{-110x} & = & \color{red}{110x} +40 \color{blue}{-110x} \color{blue}{+231} \\\Leftrightarrow & -1540x-110x& = & 40+231 \\\Leftrightarrow & \color{red}{-1650} x& = & 271 \\\Leftrightarrow & x = \frac{271}{-1650} & & \\\Leftrightarrow & x = \frac{-271}{1650} & & \\ & V = \left\{ \frac{-271}{1650} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -1350x \color{red}{-108} \color{blue}{+108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+108} \\\Leftrightarrow & -1350x+315x& = & 50+108 \\\Leftrightarrow & \color{red}{-1035} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-1035} & & \\\Leftrightarrow & x = \frac{-158}{1035} & & \\ & V = \left\{ \frac{-158}{1035} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+75} & = & \color{red}{-100x} +24 \\\Leftrightarrow & -240x \color{red}{+75} \color{blue}{-75} \color{blue}{+100x} & = & \color{red}{-100x} +24 \color{blue}{+100x} \color{blue}{-75} \\\Leftrightarrow & -240x+100x& = & 24-75 \\\Leftrightarrow & \color{red}{-140} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-140} & & \\\Leftrightarrow & x = \frac{51}{140} & & \\ & V = \left\{ \frac{51}{140} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{11})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -9x-\frac{9}{11}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{45}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-45} & = & \color{red}{-275x} +44 \\\Leftrightarrow & -495x \color{red}{-45} \color{blue}{+45} \color{blue}{+275x} & = & \color{red}{-275x} +44 \color{blue}{+275x} \color{blue}{+45} \\\Leftrightarrow & -495x+275x& = & 44+45 \\\Leftrightarrow & \color{red}{-220} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-220} & & \\\Leftrightarrow & x = \frac{-89}{220} & & \\ & V = \left\{ \frac{-89}{220} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & -924x+385x& = & 44-126 \\\Leftrightarrow & \color{red}{-539} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-539} & & \\\Leftrightarrow & x = \frac{82}{539} & & \\ & V = \left\{ \frac{82}{539} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{11})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 9x+\frac{6}{11}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 891x \color{red}{+54} & = & \color{red}{198x} +22 \\\Leftrightarrow & 891x \color{red}{+54} \color{blue}{-54} \color{blue}{-198x} & = & \color{red}{198x} +22 \color{blue}{-198x} \color{blue}{-54} \\\Leftrightarrow & 891x-198x& = & 22-54 \\\Leftrightarrow & \color{red}{693} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{693} & & \\ & V = \left\{ \frac{-32}{693} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{-147x} +28 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & 378x+147x& = & 28-90 \\\Leftrightarrow & \color{red}{525} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{525} & & \\ & V = \left\{ \frac{-62}{525} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 25x+\frac{20}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{+220} & = & \color{red}{-693x} +54 \\\Leftrightarrow & 2475x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & 2475x+693x& = & 54-220 \\\Leftrightarrow & \color{red}{3168} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{3168} & & \\\Leftrightarrow & x = \frac{-83}{1584} & & \\ & V = \left\{ \frac{-83}{1584} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{2})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{9}{2}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{63}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-63} & = & \color{red}{-98x} +20 \\\Leftrightarrow & -84x \color{red}{-63} \color{blue}{+63} \color{blue}{+98x} & = & \color{red}{-98x} +20 \color{blue}{+98x} \color{blue}{+63} \\\Leftrightarrow & -84x+98x& = & 20+63 \\\Leftrightarrow & \color{red}{14} x& = & 83 \\\Leftrightarrow & x = \frac{83}{14} & & \\ & V = \left\{ \frac{83}{14} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 16x-\frac{8}{3}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-24} & = & \color{red}{27x} +10 \\\Leftrightarrow & 144x \color{red}{-24} \color{blue}{+24} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{+24} \\\Leftrightarrow & 144x-27x& = & 10+24 \\\Leftrightarrow & \color{red}{117} x& = & 34 \\\Leftrightarrow & x = \frac{34}{117} & & \\ & V = \left\{ \frac{34}{117} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 3x+\frac{8}{5} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{+50} & = & \color{red}{105x} +56 \\\Leftrightarrow & 700x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 700x-105x& = & 56-50 \\\Leftrightarrow & \color{red}{595} x& = & 6 \\\Leftrightarrow & x = \frac{6}{595} & & \\ & V = \left\{ \frac{6}{595} \right\} & \\\end{align}\)