Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{14}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{-154} & = & \color{red}{891x} +54 \\\Leftrightarrow & 2772x \color{red}{-154} \color{blue}{+154} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{+154} \\\Leftrightarrow & 2772x-891x& = & 54+154 \\\Leftrightarrow & \color{red}{1881} x& = & 208 \\\Leftrightarrow & x = \frac{208}{1881} & & \\ & V = \left\{ \frac{208}{1881} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & -9x+\frac{9}{11} \\\Leftrightarrow & 28x+\frac{14}{9}& = & -9x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{+154} & = & \color{red}{-891x} +81 \\\Leftrightarrow & 2772x \color{red}{+154} \color{blue}{-154} \color{blue}{+891x} & = & \color{red}{-891x} +81 \color{blue}{+891x} \color{blue}{-154} \\\Leftrightarrow & 2772x+891x& = & 81-154 \\\Leftrightarrow & \color{red}{3663} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{3663} & & \\ & V = \left\{ \frac{-73}{3663} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{25}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-75} & = & \color{red}{99x} +88 \\\Leftrightarrow & 330x \color{red}{-75} \color{blue}{+75} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+75} \\\Leftrightarrow & 330x-99x& = & 88+75 \\\Leftrightarrow & \color{red}{231} x& = & 163 \\\Leftrightarrow & x = \frac{163}{231} & & \\ & V = \left\{ \frac{163}{231} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -84x+105x& = & 70-18 \\\Leftrightarrow & \color{red}{21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{405x} +40 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-405x} & = & \color{red}{405x} +40 \color{blue}{-405x} \color{blue}{+36} \\\Leftrightarrow & -180x-405x& = & 40+36 \\\Leftrightarrow & \color{red}{-585} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-585} & & \\\Leftrightarrow & x = \frac{-76}{585} & & \\ & V = \left\{ \frac{-76}{585} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{11})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{21}{11}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+63} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -1155x \color{red}{+63} \color{blue}{-63} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-63} \\\Leftrightarrow & -1155x+297x& = & 88-63 \\\Leftrightarrow & \color{red}{-858} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-858} & & \\\Leftrightarrow & x = \frac{-25}{858} & & \\ & V = \left\{ \frac{-25}{858} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{3})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x-\frac{8}{3}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-24} & = & \color{red}{-63x} +8 \\\Leftrightarrow & -54x \color{red}{-24} \color{blue}{+24} \color{blue}{+63x} & = & \color{red}{-63x} +8 \color{blue}{+63x} \color{blue}{+24} \\\Leftrightarrow & -54x+63x& = & 8+24 \\\Leftrightarrow & \color{red}{9} x& = & 32 \\\Leftrightarrow & x = \frac{32}{9} & & \\ & V = \left\{ \frac{32}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{-315x} +10 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{-84} \\\Leftrightarrow & -280x+315x& = & 10-84 \\\Leftrightarrow & \color{red}{35} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{35} & & \\ & V = \left\{ \frac{-74}{35} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 60x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{35} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{-105x} +10 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -300x+105x& = & 10+36 \\\Leftrightarrow & \color{red}{-195} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-195} & & \\\Leftrightarrow & x = \frac{-46}{195} & & \\ & V = \left\{ \frac{-46}{195} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{5}{11})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -15x+\frac{25}{11}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x+ \frac{225}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{+225} & = & \color{red}{-792x} +88 \\\Leftrightarrow & -1485x \color{red}{+225} \color{blue}{-225} \color{blue}{+792x} & = & \color{red}{-792x} +88 \color{blue}{+792x} \color{blue}{-225} \\\Leftrightarrow & -1485x+792x& = & 88-225 \\\Leftrightarrow & \color{red}{-693} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{-693} & & \\\Leftrightarrow & x = \frac{137}{693} & & \\ & V = \left\{ \frac{137}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -16x+\frac{8}{9}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{+88} & = & \color{red}{693x} +18 \\\Leftrightarrow & -1584x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +18 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & -1584x-693x& = & 18-88 \\\Leftrightarrow & \color{red}{-2277} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-2277} & & \\\Leftrightarrow & x = \frac{70}{2277} & & \\ & V = \left\{ \frac{70}{2277} \right\} & \\\end{align}\)