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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+220} & = & \color{red}{-231x} +6 \\\Leftrightarrow & -660x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +6 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & -660x+231x& = & 6-220 \\\Leftrightarrow & \color{red}{-429} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-429} & & \\\Leftrightarrow & x = \frac{214}{429} & & \\ & V = \left\{ \frac{214}{429} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{-616x} +40 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{+616x} & = & \color{red}{-616x} +40 \color{blue}{+616x} \color{blue}{+165} \\\Leftrightarrow & -880x+616x& = & 40+165 \\\Leftrightarrow & \color{red}{-264} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-264} & & \\\Leftrightarrow & x = \frac{-205}{264} & & \\ & V = \left\{ \frac{-205}{264} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{20}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-720}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -720x \color{red}{-100} & = & \color{red}{315x} +54 \\\Leftrightarrow & -720x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & -720x-315x& = & 54+100 \\\Leftrightarrow & \color{red}{-1035} x& = & 154 \\\Leftrightarrow & x = \frac{154}{-1035} & & \\\Leftrightarrow & x = \frac{-154}{1035} & & \\ & V = \left\{ \frac{-154}{1035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{5})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{245x} +20 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{-245x} & = & \color{red}{245x} +20 \color{blue}{-245x} \color{blue}{+28} \\\Leftrightarrow & -210x-245x& = & 20+28 \\\Leftrightarrow & \color{red}{-455} x& = & 48 \\\Leftrightarrow & x = \frac{48}{-455} & & \\\Leftrightarrow & x = \frac{-48}{455} & & \\ & V = \left\{ \frac{-48}{455} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -4x+\frac{6}{7}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-112}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -112x \color{red}{+24} & = & \color{red}{-140x} +49 \\\Leftrightarrow & -112x \color{red}{+24} \color{blue}{-24} \color{blue}{+140x} & = & \color{red}{-140x} +49 \color{blue}{+140x} \color{blue}{-24} \\\Leftrightarrow & -112x+140x& = & 49-24 \\\Leftrightarrow & \color{red}{28} x& = & 25 \\\Leftrightarrow & x = \frac{25}{28} & & \\ & V = \left\{ \frac{25}{28} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{49x} +4 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +4 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & -210x-49x& = & 4-30 \\\Leftrightarrow & \color{red}{-259} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-259} & & \\\Leftrightarrow & x = \frac{26}{259} & & \\ & V = \left\{ \frac{26}{259} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-60} & = & \color{red}{147x} +28 \\\Leftrightarrow & -210x \color{red}{-60} \color{blue}{+60} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+60} \\\Leftrightarrow & -210x-147x& = & 28+60 \\\Leftrightarrow & \color{red}{-357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-357} & & \\\Leftrightarrow & x = \frac{-88}{357} & & \\ & V = \left\{ \frac{-88}{357} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{315x} +42 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & 560x-315x& = & 42+100 \\\Leftrightarrow & \color{red}{245} x& = & 142 \\\Leftrightarrow & x = \frac{142}{245} & & \\ & V = \left\{ \frac{142}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{11})& = & -8x+\frac{5}{2} \\\Leftrightarrow & 21x+\frac{35}{11}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x+ \frac{70}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{+70} & = & \color{red}{-176x} +55 \\\Leftrightarrow & 462x \color{red}{+70} \color{blue}{-70} \color{blue}{+176x} & = & \color{red}{-176x} +55 \color{blue}{+176x} \color{blue}{-70} \\\Leftrightarrow & 462x+176x& = & 55-70 \\\Leftrightarrow & \color{red}{638} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{638} & & \\ & V = \left\{ \frac{-15}{638} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{9})& = & 4x+\frac{6}{11} \\\Leftrightarrow & 21x-\frac{14}{9}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x- \frac{154}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{-154} & = & \color{red}{396x} +54 \\\Leftrightarrow & 2079x \color{red}{-154} \color{blue}{+154} \color{blue}{-396x} & = & \color{red}{396x} +54 \color{blue}{-396x} \color{blue}{+154} \\\Leftrightarrow & 2079x-396x& = & 54+154 \\\Leftrightarrow & \color{red}{1683} x& = & 208 \\\Leftrightarrow & x = \frac{208}{1683} & & \\ & V = \left\{ \frac{208}{1683} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-99} & = & \color{red}{-275x} +25 \\\Leftrightarrow & -495x \color{red}{-99} \color{blue}{+99} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{+99} \\\Leftrightarrow & -495x+275x& = & 25+99 \\\Leftrightarrow & \color{red}{-220} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-220} & & \\\Leftrightarrow & x = \frac{-31}{55} & & \\ & V = \left\{ \frac{-31}{55} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{2})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -35x-\frac{21}{2}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{63}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-63} & = & \color{red}{-54x} +4 \\\Leftrightarrow & -210x \color{red}{-63} \color{blue}{+63} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{+63} \\\Leftrightarrow & -210x+54x& = & 4+63 \\\Leftrightarrow & \color{red}{-156} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-156} & & \\\Leftrightarrow & x = \frac{-67}{156} & & \\ & V = \left\{ \frac{-67}{156} \right\} & \\\end{align}\)
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