Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+14} & = & \color{red}{9x} +2 \\\Leftrightarrow & 84x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & 84x-9x& = & 2-14 \\\Leftrightarrow & \color{red}{75} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{75} & & \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-80} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -700x \color{red}{-80} \color{blue}{+80} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+80} \\\Leftrightarrow & -700x+245x& = & 28+80 \\\Leftrightarrow & \color{red}{-455} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-455} & & \\\Leftrightarrow & x = \frac{-108}{455} & & \\ & V = \left\{ \frac{-108}{455} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{9})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -20x+\frac{8}{9}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+88} & = & \color{red}{-297x} +45 \\\Leftrightarrow & -1980x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +45 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & -1980x+297x& = & 45-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-1683} & & \\\Leftrightarrow & x = \frac{43}{1683} & & \\ & V = \left\{ \frac{43}{1683} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{11})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 24x+\frac{24}{11}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+24} & = & \color{red}{-55x} +7 \\\Leftrightarrow & 264x \color{red}{+24} \color{blue}{-24} \color{blue}{+55x} & = & \color{red}{-55x} +7 \color{blue}{+55x} \color{blue}{-24} \\\Leftrightarrow & 264x+55x& = & 7-24 \\\Leftrightarrow & \color{red}{319} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{319} & & \\ & V = \left\{ \frac{-17}{319} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & 6x+\frac{6}{11} \\\Leftrightarrow & 35x-\frac{35}{9}& = & 6x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-385} & = & \color{red}{594x} +54 \\\Leftrightarrow & 3465x \color{red}{-385} \color{blue}{+385} \color{blue}{-594x} & = & \color{red}{594x} +54 \color{blue}{-594x} \color{blue}{+385} \\\Leftrightarrow & 3465x-594x& = & 54+385 \\\Leftrightarrow & \color{red}{2871} x& = & 439 \\\Leftrightarrow & x = \frac{439}{2871} & & \\ & V = \left\{ \frac{439}{2871} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{8})& = & 6x+\frac{4}{9} \\\Leftrightarrow & 25x+\frac{25}{8}& = & 6x+\frac{4}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1800}{ \color{blue}{72} }x+ \frac{225}{ \color{blue}{72} })& = & (\frac{432}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1800x \color{red}{+225} & = & \color{red}{432x} +32 \\\Leftrightarrow & 1800x \color{red}{+225} \color{blue}{-225} \color{blue}{-432x} & = & \color{red}{432x} +32 \color{blue}{-432x} \color{blue}{-225} \\\Leftrightarrow & 1800x-432x& = & 32-225 \\\Leftrightarrow & \color{red}{1368} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{1368} & & \\ & V = \left\{ \frac{-193}{1368} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+60} & = & \color{red}{63x} +14 \\\Leftrightarrow & 420x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & 420x-63x& = & 14-60 \\\Leftrightarrow & \color{red}{357} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{357} & & \\ & V = \left\{ \frac{-46}{357} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -18x-\frac{24}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-24} & = & \color{red}{-55x} +10 \\\Leftrightarrow & -198x \color{red}{-24} \color{blue}{+24} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{+24} \\\Leftrightarrow & -198x+55x& = & 10+24 \\\Leftrightarrow & \color{red}{-143} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-143} & & \\\Leftrightarrow & x = \frac{-34}{143} & & \\ & V = \left\{ \frac{-34}{143} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{3}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x- \frac{20}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{-20} & = & \color{red}{75x} +18 \\\Leftrightarrow & 90x \color{red}{-20} \color{blue}{+20} \color{blue}{-75x} & = & \color{red}{75x} +18 \color{blue}{-75x} \color{blue}{+20} \\\Leftrightarrow & 90x-75x& = & 18+20 \\\Leftrightarrow & \color{red}{15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{15} & & \\ & V = \left\{ \frac{38}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-105} & = & \color{red}{-99x} +88 \\\Leftrightarrow & -1155x \color{red}{-105} \color{blue}{+105} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{+105} \\\Leftrightarrow & -1155x+99x& = & 88+105 \\\Leftrightarrow & \color{red}{-1056} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-1056} & & \\\Leftrightarrow & x = \frac{-193}{1056} & & \\ & V = \left\{ \frac{-193}{1056} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{15}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{150}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+150} & = & \color{red}{770x} +33 \\\Leftrightarrow & 1320x \color{red}{+150} \color{blue}{-150} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{-150} \\\Leftrightarrow & 1320x-770x& = & 33-150 \\\Leftrightarrow & \color{red}{550} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{550} & & \\ & V = \left\{ \frac{-117}{550} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{11})& = & 4x+\frac{4}{9} \\\Leftrightarrow & 15x+\frac{25}{11}& = & 4x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1485}{ \color{blue}{99} }x+ \frac{225}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1485x \color{red}{+225} & = & \color{red}{396x} +44 \\\Leftrightarrow & 1485x \color{red}{+225} \color{blue}{-225} \color{blue}{-396x} & = & \color{red}{396x} +44 \color{blue}{-396x} \color{blue}{-225} \\\Leftrightarrow & 1485x-396x& = & 44-225 \\\Leftrightarrow & \color{red}{1089} x& = & -181 \\\Leftrightarrow & x = \frac{-181}{1089} & & \\ & V = \left\{ \frac{-181}{1089} \right\} & \\\end{align}\)