Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{5})& = & 4x+\frac{5}{4} \\\Leftrightarrow & 21x-\frac{14}{5}& = & 4x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{420}{ \color{blue}{20} }x- \frac{56}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 420x \color{red}{-56} & = & \color{red}{80x} +25 \\\Leftrightarrow & 420x \color{red}{-56} \color{blue}{+56} \color{blue}{-80x} & = & \color{red}{80x} +25 \color{blue}{-80x} \color{blue}{+56} \\\Leftrightarrow & 420x-80x& = & 25+56 \\\Leftrightarrow & \color{red}{340} x& = & 81 \\\Leftrightarrow & x = \frac{81}{340} & & \\ & V = \left\{ \frac{81}{340} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-6} & = & \color{red}{-40x} +6 \\\Leftrightarrow & -75x \color{red}{-6} \color{blue}{+6} \color{blue}{+40x} & = & \color{red}{-40x} +6 \color{blue}{+40x} \color{blue}{+6} \\\Leftrightarrow & -75x+40x& = & 6+6 \\\Leftrightarrow & \color{red}{-35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-35} & & \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{2}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{4}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-28} & = & \color{red}{539x} +44 \\\Leftrightarrow & 770x \color{red}{-28} \color{blue}{+28} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+28} \\\Leftrightarrow & 770x-539x& = & 44+28 \\\Leftrightarrow & \color{red}{231} x& = & 72 \\\Leftrightarrow & x = \frac{72}{231} & & \\\Leftrightarrow & x = \frac{24}{77} & & \\ & V = \left\{ \frac{24}{77} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -28x-\frac{14}{3}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{-42} & = & \color{red}{72x} +10 \\\Leftrightarrow & -252x \color{red}{-42} \color{blue}{+42} \color{blue}{-72x} & = & \color{red}{72x} +10 \color{blue}{-72x} \color{blue}{+42} \\\Leftrightarrow & -252x-72x& = & 10+42 \\\Leftrightarrow & \color{red}{-324} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-324} & & \\\Leftrightarrow & x = \frac{-13}{81} & & \\ & V = \left\{ \frac{-13}{81} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{7})& = & -3x+\frac{9}{5} \\\Leftrightarrow & 10x-\frac{6}{7}& = & -3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-30} & = & \color{red}{-105x} +63 \\\Leftrightarrow & 350x \color{red}{-30} \color{blue}{+30} \color{blue}{+105x} & = & \color{red}{-105x} +63 \color{blue}{+105x} \color{blue}{+30} \\\Leftrightarrow & 350x+105x& = & 63+30 \\\Leftrightarrow & \color{red}{455} x& = & 93 \\\Leftrightarrow & x = \frac{93}{455} & & \\ & V = \left\{ \frac{93}{455} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{-70x} +25 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +25 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & -300x+70x& = & 25-24 \\\Leftrightarrow & \color{red}{-230} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-230} & & \\\Leftrightarrow & x = \frac{-1}{230} & & \\ & V = \left\{ \frac{-1}{230} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-50} & = & \color{red}{245x} +42 \\\Leftrightarrow & -700x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & -700x-245x& = & 42+50 \\\Leftrightarrow & \color{red}{-945} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-945} & & \\\Leftrightarrow & x = \frac{-92}{945} & & \\ & V = \left\{ \frac{-92}{945} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 4x+\frac{9}{2} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{40x} +45 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{-40x} & = & \color{red}{40x} +45 \color{blue}{-40x} \color{blue}{+24} \\\Leftrightarrow & 90x-40x& = & 45+24 \\\Leftrightarrow & \color{red}{50} x& = & 69 \\\Leftrightarrow & x = \frac{69}{50} & & \\ & V = \left\{ \frac{69}{50} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & 630x+175x& = & 28+150 \\\Leftrightarrow & \color{red}{805} x& = & 178 \\\Leftrightarrow & x = \frac{178}{805} & & \\ & V = \left\{ \frac{178}{805} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{12})& = & 2x+\frac{6}{11} \\\Leftrightarrow & 21x+\frac{35}{12}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2772}{ \color{blue}{132} }x+ \frac{385}{ \color{blue}{132} })& = & (\frac{264}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2772x \color{red}{+385} & = & \color{red}{264x} +72 \\\Leftrightarrow & 2772x \color{red}{+385} \color{blue}{-385} \color{blue}{-264x} & = & \color{red}{264x} +72 \color{blue}{-264x} \color{blue}{-385} \\\Leftrightarrow & 2772x-264x& = & 72-385 \\\Leftrightarrow & \color{red}{2508} x& = & -313 \\\Leftrightarrow & x = \frac{-313}{2508} & & \\ & V = \left\{ \frac{-313}{2508} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{2})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+175} & = & \color{red}{-28x} +16 \\\Leftrightarrow & 350x \color{red}{+175} \color{blue}{-175} \color{blue}{+28x} & = & \color{red}{-28x} +16 \color{blue}{+28x} \color{blue}{-175} \\\Leftrightarrow & 350x+28x& = & 16-175 \\\Leftrightarrow & \color{red}{378} x& = & -159 \\\Leftrightarrow & x = \frac{-159}{378} & & \\\Leftrightarrow & x = \frac{-53}{126} & & \\ & V = \left\{ \frac{-53}{126} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -30x+\frac{24}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x+ \frac{240}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{+240} & = & \color{red}{770x} +99 \\\Leftrightarrow & -3300x \color{red}{+240} \color{blue}{-240} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{-240} \\\Leftrightarrow & -3300x-770x& = & 99-240 \\\Leftrightarrow & \color{red}{-4070} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-4070} & & \\\Leftrightarrow & x = \frac{141}{4070} & & \\ & V = \left\{ \frac{141}{4070} \right\} & \\\end{align}\)
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