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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -18x+\frac{12}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1980}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1980x \color{red}{+120} & = & \color{red}{550x} +33 \\\Leftrightarrow & -1980x \color{red}{+120} \color{blue}{-120} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{-120} \\\Leftrightarrow & -1980x-550x& = & 33-120 \\\Leftrightarrow & \color{red}{-2530} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-2530} & & \\\Leftrightarrow & x = \frac{87}{2530} & & \\ & V = \left\{ \frac{87}{2530} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -9x+\frac{9}{8} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{-96} & = & \color{red}{-360x} +45 \\\Leftrightarrow & -320x \color{red}{-96} \color{blue}{+96} \color{blue}{+360x} & = & \color{red}{-360x} +45 \color{blue}{+360x} \color{blue}{+96} \\\Leftrightarrow & -320x+360x& = & 45+96 \\\Leftrightarrow & \color{red}{40} x& = & 141 \\\Leftrightarrow & x = \frac{141}{40} & & \\ & V = \left\{ \frac{141}{40} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{5})& = & -6x+\frac{5}{11} \\\Leftrightarrow & -35x-\frac{28}{5}& = & -6x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-330}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-308} & = & \color{red}{-330x} +25 \\\Leftrightarrow & -1925x \color{red}{-308} \color{blue}{+308} \color{blue}{+330x} & = & \color{red}{-330x} +25 \color{blue}{+330x} \color{blue}{+308} \\\Leftrightarrow & -1925x+330x& = & 25+308 \\\Leftrightarrow & \color{red}{-1595} x& = & 333 \\\Leftrightarrow & x = \frac{333}{-1595} & & \\\Leftrightarrow & x = \frac{-333}{1595} & & \\ & V = \left\{ \frac{-333}{1595} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1152}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1152x \color{red}{-64} & = & \color{red}{504x} +27 \\\Leftrightarrow & 1152x \color{red}{-64} \color{blue}{+64} \color{blue}{-504x} & = & \color{red}{504x} +27 \color{blue}{-504x} \color{blue}{+64} \\\Leftrightarrow & 1152x-504x& = & 27+64 \\\Leftrightarrow & \color{red}{648} x& = & 91 \\\Leftrightarrow & x = \frac{91}{648} & & \\ & V = \left\{ \frac{91}{648} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 4x+\frac{8}{7} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-84} & = & \color{red}{140x} +40 \\\Leftrightarrow & -630x \color{red}{-84} \color{blue}{+84} \color{blue}{-140x} & = & \color{red}{140x} +40 \color{blue}{-140x} \color{blue}{+84} \\\Leftrightarrow & -630x-140x& = & 40+84 \\\Leftrightarrow & \color{red}{-770} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-770} & & \\\Leftrightarrow & x = \frac{-62}{385} & & \\ & V = \left\{ \frac{-62}{385} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+54} & = & \color{red}{495x} +110 \\\Leftrightarrow & 594x \color{red}{+54} \color{blue}{-54} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{-54} \\\Leftrightarrow & 594x-495x& = & 110-54 \\\Leftrightarrow & \color{red}{99} x& = & 56 \\\Leftrightarrow & x = \frac{56}{99} & & \\ & V = \left\{ \frac{56}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -120x+50x& = & 15+24 \\\Leftrightarrow & \color{red}{-70} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-70} & & \\\Leftrightarrow & x = \frac{-39}{70} & & \\ & V = \left\{ \frac{-39}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 8x+\frac{7}{10} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 8x+\frac{7}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{28}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{+105} & = & \color{red}{320x} +28 \\\Leftrightarrow & 1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-320x} & = & \color{red}{320x} +28 \color{blue}{-320x} \color{blue}{-105} \\\Leftrightarrow & 1400x-320x& = & 28-105 \\\Leftrightarrow & \color{red}{1080} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{1080} & & \\ & V = \left\{ \frac{-77}{1080} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & 378x+147x& = & 70-90 \\\Leftrightarrow & \color{red}{525} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{525} & & \\\Leftrightarrow & x = \frac{-4}{105} & & \\ & V = \left\{ \frac{-4}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 9x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x+ \frac{64}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{+64} & = & \color{red}{396x} +33 \\\Leftrightarrow & 352x \color{red}{+64} \color{blue}{-64} \color{blue}{-396x} & = & \color{red}{396x} +33 \color{blue}{-396x} \color{blue}{-64} \\\Leftrightarrow & 352x-396x& = & 33-64 \\\Leftrightarrow & \color{red}{-44} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-44} & & \\\Leftrightarrow & x = \frac{31}{44} & & \\ & V = \left\{ \frac{31}{44} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{693x} +42 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{+110} \\\Leftrightarrow & 770x-693x& = & 42+110 \\\Leftrightarrow & \color{red}{77} x& = & 152 \\\Leftrightarrow & x = \frac{152}{77} & & \\ & V = \left\{ \frac{152}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{6})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -14x-\frac{35}{6}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-924}{ \color{blue}{66} }x- \frac{385}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{12}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -924x \color{red}{-385} & = & \color{red}{-198x} +12 \\\Leftrightarrow & -924x \color{red}{-385} \color{blue}{+385} \color{blue}{+198x} & = & \color{red}{-198x} +12 \color{blue}{+198x} \color{blue}{+385} \\\Leftrightarrow & -924x+198x& = & 12+385 \\\Leftrightarrow & \color{red}{-726} x& = & 397 \\\Leftrightarrow & x = \frac{397}{-726} & & \\\Leftrightarrow & x = \frac{-397}{726} & & \\ & V = \left\{ \frac{-397}{726} \right\} & \\\end{align}\)
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