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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{11})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{8}{11}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+40} & = & \color{red}{495x} +88 \\\Leftrightarrow & -440x \color{red}{+40} \color{blue}{-40} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-40} \\\Leftrightarrow & -440x-495x& = & 88-40 \\\Leftrightarrow & \color{red}{-935} x& = & 48 \\\Leftrightarrow & x = \frac{48}{-935} & & \\\Leftrightarrow & x = \frac{-48}{935} & & \\ & V = \left\{ \frac{-48}{935} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{5})& = & -8x+\frac{9}{2} \\\Leftrightarrow & -28x+\frac{14}{5}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x+ \frac{28}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{+28} & = & \color{red}{-80x} +45 \\\Leftrightarrow & -280x \color{red}{+28} \color{blue}{-28} \color{blue}{+80x} & = & \color{red}{-80x} +45 \color{blue}{+80x} \color{blue}{-28} \\\Leftrightarrow & -280x+80x& = & 45-28 \\\Leftrightarrow & \color{red}{-200} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-200} & & \\\Leftrightarrow & x = \frac{-17}{200} & & \\ & V = \left\{ \frac{-17}{200} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -15x-\frac{20}{9}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-140} & = & \color{red}{504x} +90 \\\Leftrightarrow & -945x \color{red}{-140} \color{blue}{+140} \color{blue}{-504x} & = & \color{red}{504x} +90 \color{blue}{-504x} \color{blue}{+140} \\\Leftrightarrow & -945x-504x& = & 90+140 \\\Leftrightarrow & \color{red}{-1449} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1449} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{11})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 12x+\frac{30}{11}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x+ \frac{300}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{+300} & = & \color{red}{-550x} +99 \\\Leftrightarrow & 1320x \color{red}{+300} \color{blue}{-300} \color{blue}{+550x} & = & \color{red}{-550x} +99 \color{blue}{+550x} \color{blue}{-300} \\\Leftrightarrow & 1320x+550x& = & 99-300 \\\Leftrightarrow & \color{red}{1870} x& = & -201 \\\Leftrightarrow & x = \frac{-201}{1870} & & \\ & V = \left\{ \frac{-201}{1870} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+30} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{+30} \color{blue}{-30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-30} \\\Leftrightarrow & -420x-175x& = & 42-30 \\\Leftrightarrow & \color{red}{-595} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-595} & & \\\Leftrightarrow & x = \frac{-12}{595} & & \\ & V = \left\{ \frac{-12}{595} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{2})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{350}{ \color{blue}{14} }x+ \frac{175}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 350x \color{red}{+175} & = & \color{red}{-98x} +12 \\\Leftrightarrow & 350x \color{red}{+175} \color{blue}{-175} \color{blue}{+98x} & = & \color{red}{-98x} +12 \color{blue}{+98x} \color{blue}{-175} \\\Leftrightarrow & 350x+98x& = & 12-175 \\\Leftrightarrow & \color{red}{448} x& = & -163 \\\Leftrightarrow & x = \frac{-163}{448} & & \\ & V = \left\{ \frac{-163}{448} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{-66} \\\Leftrightarrow & 616x+231x& = & 42-66 \\\Leftrightarrow & \color{red}{847} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{847} & & \\ & V = \left\{ \frac{-24}{847} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{11})& = & -7x+\frac{5}{9} \\\Leftrightarrow & -9x-\frac{12}{11}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-891}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -891x \color{red}{-108} & = & \color{red}{-693x} +55 \\\Leftrightarrow & -891x \color{red}{-108} \color{blue}{+108} \color{blue}{+693x} & = & \color{red}{-693x} +55 \color{blue}{+693x} \color{blue}{+108} \\\Leftrightarrow & -891x+693x& = & 55+108 \\\Leftrightarrow & \color{red}{-198} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-198} & & \\\Leftrightarrow & x = \frac{-163}{198} & & \\ & V = \left\{ \frac{-163}{198} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{12}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+60} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 660x \color{red}{+60} \color{blue}{-60} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-60} \\\Leftrightarrow & 660x+275x& = & 66-60 \\\Leftrightarrow & \color{red}{935} x& = & 6 \\\Leftrightarrow & x = \frac{6}{935} & & \\ & V = \left\{ \frac{6}{935} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{1}{2})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{5}{2}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{15}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-15} & = & \color{red}{42x} +16 \\\Leftrightarrow & 60x \color{red}{-15} \color{blue}{+15} \color{blue}{-42x} & = & \color{red}{42x} +16 \color{blue}{-42x} \color{blue}{+15} \\\Leftrightarrow & 60x-42x& = & 16+15 \\\Leftrightarrow & \color{red}{18} x& = & 31 \\\Leftrightarrow & x = \frac{31}{18} & & \\ & V = \left\{ \frac{31}{18} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{7})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{189x} +70 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{-18} \\\Leftrightarrow & -84x-189x& = & 70-18 \\\Leftrightarrow & \color{red}{-273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-273} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{5})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{+44} & = & \color{red}{495x} +50 \\\Leftrightarrow & -440x \color{red}{+44} \color{blue}{-44} \color{blue}{-495x} & = & \color{red}{495x} +50 \color{blue}{-495x} \color{blue}{-44} \\\Leftrightarrow & -440x-495x& = & 50-44 \\\Leftrightarrow & \color{red}{-935} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-935} & & \\\Leftrightarrow & x = \frac{-6}{935} & & \\ & V = \left\{ \frac{-6}{935} \right\} & \\\end{align}\)
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