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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -4x+\frac{9}{7} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-6} & = & \color{red}{-28x} +9 \\\Leftrightarrow & 105x \color{red}{-6} \color{blue}{+6} \color{blue}{+28x} & = & \color{red}{-28x} +9 \color{blue}{+28x} \color{blue}{+6} \\\Leftrightarrow & 105x+28x& = & 9+6 \\\Leftrightarrow & \color{red}{133} x& = & 15 \\\Leftrightarrow & x = \frac{15}{133} & & \\ & V = \left\{ \frac{15}{133} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & 150x+70x& = & 15-24 \\\Leftrightarrow & \color{red}{220} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{220} & & \\ & V = \left\{ \frac{-9}{220} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{9})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+20} & = & \color{red}{63x} +10 \\\Leftrightarrow & -144x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -144x-63x& = & 10-20 \\\Leftrightarrow & \color{red}{-207} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-207} & & \\\Leftrightarrow & x = \frac{10}{207} & & \\ & V = \left\{ \frac{10}{207} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-20} & = & \color{red}{-21x} +4 \\\Leftrightarrow & -60x \color{red}{-20} \color{blue}{+20} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{+20} \\\Leftrightarrow & -60x+21x& = & 4+20 \\\Leftrightarrow & \color{red}{-39} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-39} & & \\\Leftrightarrow & x = \frac{-8}{13} & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{9})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{20}{9}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{216}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 216x \color{red}{+40} & = & \color{red}{126x} +27 \\\Leftrightarrow & 216x \color{red}{+40} \color{blue}{-40} \color{blue}{-126x} & = & \color{red}{126x} +27 \color{blue}{-126x} \color{blue}{-40} \\\Leftrightarrow & 216x-126x& = & 27-40 \\\Leftrightarrow & \color{red}{90} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{90} & & \\ & V = \left\{ \frac{-13}{90} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{10})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 14x+\frac{21}{10}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{980}{ \color{blue}{70} }x+ \frac{147}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{40}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 980x \color{red}{+147} & = & \color{red}{-630x} +40 \\\Leftrightarrow & 980x \color{red}{+147} \color{blue}{-147} \color{blue}{+630x} & = & \color{red}{-630x} +40 \color{blue}{+630x} \color{blue}{-147} \\\Leftrightarrow & 980x+630x& = & 40-147 \\\Leftrightarrow & \color{red}{1610} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{1610} & & \\ & V = \left\{ \frac{-107}{1610} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -14x-\frac{14}{9}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-14} & = & \color{red}{-27x} +8 \\\Leftrightarrow & -126x \color{red}{-14} \color{blue}{+14} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{+14} \\\Leftrightarrow & -126x+27x& = & 8+14 \\\Leftrightarrow & \color{red}{-99} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-99} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{3})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{25}{3}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{175}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-175} & = & \color{red}{147x} +27 \\\Leftrightarrow & -210x \color{red}{-175} \color{blue}{+175} \color{blue}{-147x} & = & \color{red}{147x} +27 \color{blue}{-147x} \color{blue}{+175} \\\Leftrightarrow & -210x-147x& = & 27+175 \\\Leftrightarrow & \color{red}{-357} x& = & 202 \\\Leftrightarrow & x = \frac{202}{-357} & & \\\Leftrightarrow & x = \frac{-202}{357} & & \\ & V = \left\{ \frac{-202}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & -2x+\frac{10}{7} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{-105} & = & \color{red}{-56x} +40 \\\Leftrightarrow & -700x \color{red}{-105} \color{blue}{+105} \color{blue}{+56x} & = & \color{red}{-56x} +40 \color{blue}{+56x} \color{blue}{+105} \\\Leftrightarrow & -700x+56x& = & 40+105 \\\Leftrightarrow & \color{red}{-644} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-644} & & \\\Leftrightarrow & x = \frac{-145}{644} & & \\ & V = \left\{ \frac{-145}{644} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{5}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 18x+\frac{30}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+330} & = & \color{red}{539x} +28 \\\Leftrightarrow & 1386x \color{red}{+330} \color{blue}{-330} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{-330} \\\Leftrightarrow & 1386x-539x& = & 28-330 \\\Leftrightarrow & \color{red}{847} x& = & -302 \\\Leftrightarrow & x = \frac{-302}{847} & & \\ & V = \left\{ \frac{-302}{847} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{8})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{15}{8}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1320x \color{red}{+165} & = & \color{red}{704x} +80 \\\Leftrightarrow & -1320x \color{red}{+165} \color{blue}{-165} \color{blue}{-704x} & = & \color{red}{704x} +80 \color{blue}{-704x} \color{blue}{-165} \\\Leftrightarrow & -1320x-704x& = & 80-165 \\\Leftrightarrow & \color{red}{-2024} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-2024} & & \\\Leftrightarrow & x = \frac{85}{2024} & & \\ & V = \left\{ \frac{85}{2024} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & -6x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -6x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{+90} & = & \color{red}{-126x} +56 \\\Leftrightarrow & -378x \color{red}{+90} \color{blue}{-90} \color{blue}{+126x} & = & \color{red}{-126x} +56 \color{blue}{+126x} \color{blue}{-90} \\\Leftrightarrow & -378x+126x& = & 56-90 \\\Leftrightarrow & \color{red}{-252} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-252} & & \\\Leftrightarrow & x = \frac{17}{126} & & \\ & V = \left\{ \frac{17}{126} \right\} & \\\end{align}\)
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