Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{7})& = & 2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 2x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{28}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-12} & = & \color{red}{28x} +63 \\\Leftrightarrow & 210x \color{red}{-12} \color{blue}{+12} \color{blue}{-28x} & = & \color{red}{28x} +63 \color{blue}{-28x} \color{blue}{+12} \\\Leftrightarrow & 210x-28x& = & 63+12 \\\Leftrightarrow & \color{red}{182} x& = & 75 \\\Leftrightarrow & x = \frac{75}{182} & & \\ & V = \left\{ \frac{75}{182} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 126x+105x& = & 14+18 \\\Leftrightarrow & \color{red}{231} x& = & 32 \\\Leftrightarrow & x = \frac{32}{231} & & \\ & V = \left\{ \frac{32}{231} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1512}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1512x \color{red}{+189} & = & \color{red}{-360x} +64 \\\Leftrightarrow & 1512x \color{red}{+189} \color{blue}{-189} \color{blue}{+360x} & = & \color{red}{-360x} +64 \color{blue}{+360x} \color{blue}{-189} \\\Leftrightarrow & 1512x+360x& = & 64-189 \\\Leftrightarrow & \color{red}{1872} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1872} & & \\ & V = \left\{ \frac{-125}{1872} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{7})& = & 6x+\frac{9}{2} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 6x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{84}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{-40} & = & \color{red}{84x} +63 \\\Leftrightarrow & -350x \color{red}{-40} \color{blue}{+40} \color{blue}{-84x} & = & \color{red}{84x} +63 \color{blue}{-84x} \color{blue}{+40} \\\Leftrightarrow & -350x-84x& = & 63+40 \\\Leftrightarrow & \color{red}{-434} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-434} & & \\\Leftrightarrow & x = \frac{-103}{434} & & \\ & V = \left\{ \frac{-103}{434} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-800}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -800x \color{red}{+96} & = & \color{red}{280x} +45 \\\Leftrightarrow & -800x \color{red}{+96} \color{blue}{-96} \color{blue}{-280x} & = & \color{red}{280x} +45 \color{blue}{-280x} \color{blue}{-96} \\\Leftrightarrow & -800x-280x& = & 45-96 \\\Leftrightarrow & \color{red}{-1080} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{-1080} & & \\\Leftrightarrow & x = \frac{17}{360} & & \\ & V = \left\{ \frac{17}{360} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-20} & = & \color{red}{21x} +4 \\\Leftrightarrow & -60x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & -60x-21x& = & 4+20 \\\Leftrightarrow & \color{red}{-81} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-81} & & \\\Leftrightarrow & x = \frac{-8}{27} & & \\ & V = \left\{ \frac{-8}{27} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+40} & = & \color{red}{84x} +63 \\\Leftrightarrow & -560x \color{red}{+40} \color{blue}{-40} \color{blue}{-84x} & = & \color{red}{84x} +63 \color{blue}{-84x} \color{blue}{-40} \\\Leftrightarrow & -560x-84x& = & 63-40 \\\Leftrightarrow & \color{red}{-644} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-644} & & \\\Leftrightarrow & x = \frac{-1}{28} & & \\ & V = \left\{ \frac{-1}{28} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{2})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{15}{2}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{24}{ \color{blue}{2} }x+ \frac{15}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 24x \color{red}{+15} & = & \color{red}{-10x} +5 \\\Leftrightarrow & 24x \color{red}{+15} \color{blue}{-15} \color{blue}{+10x} & = & \color{red}{-10x} +5 \color{blue}{+10x} \color{blue}{-15} \\\Leftrightarrow & 24x+10x& = & 5-15 \\\Leftrightarrow & \color{red}{34} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{34} & & \\\Leftrightarrow & x = \frac{-5}{17} & & \\ & V = \left\{ \frac{-5}{17} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{11})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -20x+\frac{20}{11}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1320}{ \color{blue}{66} }x+ \frac{120}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{462x} +77 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{-462x} & = & \color{red}{462x} +77 \color{blue}{-462x} \color{blue}{-120} \\\Leftrightarrow & -1320x-462x& = & 77-120 \\\Leftrightarrow & \color{red}{-1782} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-1782} & & \\\Leftrightarrow & x = \frac{43}{1782} & & \\ & V = \left\{ \frac{43}{1782} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{10}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+110} & = & \color{red}{-539x} +28 \\\Leftrightarrow & 1155x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & 1155x+539x& = & 28-110 \\\Leftrightarrow & \color{red}{1694} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{1694} & & \\\Leftrightarrow & x = \frac{-41}{847} & & \\ & V = \left\{ \frac{-41}{847} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x-\frac{4}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{20}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-20} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -550x \color{red}{-20} \color{blue}{+20} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+20} \\\Leftrightarrow & -550x+385x& = & 22+20 \\\Leftrightarrow & \color{red}{-165} x& = & 42 \\\Leftrightarrow & x = \frac{42}{-165} & & \\\Leftrightarrow & x = \frac{-14}{55} & & \\ & V = \left\{ \frac{-14}{55} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{5})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{6}{5}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+42} & = & \color{red}{-315x} +15 \\\Leftrightarrow & 350x \color{red}{+42} \color{blue}{-42} \color{blue}{+315x} & = & \color{red}{-315x} +15 \color{blue}{+315x} \color{blue}{-42} \\\Leftrightarrow & 350x+315x& = & 15-42 \\\Leftrightarrow & \color{red}{665} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{665} & & \\ & V = \left\{ \frac{-27}{665} \right\} & \\\end{align}\)
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