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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 4x-\frac{4}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-28} & = & \color{red}{-539x} +110 \\\Leftrightarrow & 308x \color{red}{-28} \color{blue}{+28} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+28} \\\Leftrightarrow & 308x+539x& = & 110+28 \\\Leftrightarrow & \color{red}{847} x& = & 138 \\\Leftrightarrow & x = \frac{138}{847} & & \\ & V = \left\{ \frac{138}{847} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 60x+50x& = & 35-24 \\\Leftrightarrow & \color{red}{110} x& = & 11 \\\Leftrightarrow & x = \frac{11}{110} & & \\\Leftrightarrow & x = \frac{1}{10} & & \\ & V = \left\{ \frac{1}{10} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & 8x+\frac{6}{7} \\\Leftrightarrow & -21x+\frac{28}{3}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+196} & = & \color{red}{168x} +18 \\\Leftrightarrow & -441x \color{red}{+196} \color{blue}{-196} \color{blue}{-168x} & = & \color{red}{168x} +18 \color{blue}{-168x} \color{blue}{-196} \\\Leftrightarrow & -441x-168x& = & 18-196 \\\Leftrightarrow & \color{red}{-609} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{-609} & & \\\Leftrightarrow & x = \frac{178}{609} & & \\ & V = \left\{ \frac{178}{609} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{8})& = & 2x+\frac{8}{9} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 2x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{648}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{144}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 648x \color{red}{+135} & = & \color{red}{144x} +64 \\\Leftrightarrow & 648x \color{red}{+135} \color{blue}{-135} \color{blue}{-144x} & = & \color{red}{144x} +64 \color{blue}{-144x} \color{blue}{-135} \\\Leftrightarrow & 648x-144x& = & 64-135 \\\Leftrightarrow & \color{red}{504} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{504} & & \\ & V = \left\{ \frac{-71}{504} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-48} \\\Leftrightarrow & -240x+50x& = & 15-48 \\\Leftrightarrow & \color{red}{-190} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-190} & & \\\Leftrightarrow & x = \frac{33}{190} & & \\ & V = \left\{ \frac{33}{190} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{11})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -35x-\frac{35}{11}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{-245} & = & \color{red}{-693x} +44 \\\Leftrightarrow & -2695x \color{red}{-245} \color{blue}{+245} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{+245} \\\Leftrightarrow & -2695x+693x& = & 44+245 \\\Leftrightarrow & \color{red}{-2002} x& = & 289 \\\Leftrightarrow & x = \frac{289}{-2002} & & \\\Leftrightarrow & x = \frac{-289}{2002} & & \\ & V = \left\{ \frac{-289}{2002} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-84} & = & \color{red}{-245x} +40 \\\Leftrightarrow & 700x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +40 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 700x+245x& = & 40+84 \\\Leftrightarrow & \color{red}{945} x& = & 124 \\\Leftrightarrow & x = \frac{124}{945} & & \\ & V = \left\{ \frac{124}{945} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-640}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -640x \color{red}{-96} & = & \color{red}{280x} +25 \\\Leftrightarrow & -640x \color{red}{-96} \color{blue}{+96} \color{blue}{-280x} & = & \color{red}{280x} +25 \color{blue}{-280x} \color{blue}{+96} \\\Leftrightarrow & -640x-280x& = & 25+96 \\\Leftrightarrow & \color{red}{-920} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-920} & & \\\Leftrightarrow & x = \frac{-121}{920} & & \\ & V = \left\{ \frac{-121}{920} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-192}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -192x \color{red}{+32} & = & \color{red}{-84x} +27 \\\Leftrightarrow & -192x \color{red}{+32} \color{blue}{-32} \color{blue}{+84x} & = & \color{red}{-84x} +27 \color{blue}{+84x} \color{blue}{-32} \\\Leftrightarrow & -192x+84x& = & 27-32 \\\Leftrightarrow & \color{red}{-108} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-108} & & \\\Leftrightarrow & x = \frac{5}{108} & & \\ & V = \left\{ \frac{5}{108} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & -8x+\frac{6}{7} \\\Leftrightarrow & -28x-\frac{14}{5}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{-98} & = & \color{red}{-280x} +30 \\\Leftrightarrow & -980x \color{red}{-98} \color{blue}{+98} \color{blue}{+280x} & = & \color{red}{-280x} +30 \color{blue}{+280x} \color{blue}{+98} \\\Leftrightarrow & -980x+280x& = & 30+98 \\\Leftrightarrow & \color{red}{-700} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-700} & & \\\Leftrightarrow & x = \frac{-32}{175} & & \\ & V = \left\{ \frac{-32}{175} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{-245} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-245} & & \\\Leftrightarrow & x = \frac{-99}{245} & & \\ & V = \left\{ \frac{-99}{245} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+110} & = & \color{red}{308x} +70 \\\Leftrightarrow & -1155x \color{red}{+110} \color{blue}{-110} \color{blue}{-308x} & = & \color{red}{308x} +70 \color{blue}{-308x} \color{blue}{-110} \\\Leftrightarrow & -1155x-308x& = & 70-110 \\\Leftrightarrow & \color{red}{-1463} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1463} & & \\\Leftrightarrow & x = \frac{40}{1463} & & \\ & V = \left\{ \frac{40}{1463} \right\} & \\\end{align}\)
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