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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{10}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-110} & = & \color{red}{231x} +18 \\\Leftrightarrow & -198x \color{red}{-110} \color{blue}{+110} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+110} \\\Leftrightarrow & -198x-231x& = & 18+110 \\\Leftrightarrow & \color{red}{-429} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-429} & & \\\Leftrightarrow & x = \frac{-128}{429} & & \\ & V = \left\{ \frac{-128}{429} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{9})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 16x+\frac{20}{9}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{576}{ \color{blue}{36} }x+ \frac{80}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 576x \color{red}{+80} & = & \color{red}{-180x} +27 \\\Leftrightarrow & 576x \color{red}{+80} \color{blue}{-80} \color{blue}{+180x} & = & \color{red}{-180x} +27 \color{blue}{+180x} \color{blue}{-80} \\\Leftrightarrow & 576x+180x& = & 27-80 \\\Leftrightarrow & \color{red}{756} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{756} & & \\ & V = \left\{ \frac{-53}{756} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{3})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -10x-\frac{20}{3}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-220} & = & \color{red}{231x} +12 \\\Leftrightarrow & -330x \color{red}{-220} \color{blue}{+220} \color{blue}{-231x} & = & \color{red}{231x} +12 \color{blue}{-231x} \color{blue}{+220} \\\Leftrightarrow & -330x-231x& = & 12+220 \\\Leftrightarrow & \color{red}{-561} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-561} & & \\\Leftrightarrow & x = \frac{-232}{561} & & \\ & V = \left\{ \frac{-232}{561} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{+45} & = & \color{red}{84x} +40 \\\Leftrightarrow & -72x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +40 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & -72x-84x& = & 40-45 \\\Leftrightarrow & \color{red}{-156} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-156} & & \\\Leftrightarrow & x = \frac{5}{156} & & \\ & V = \left\{ \frac{5}{156} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{10}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-440}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -440x \color{red}{-100} & = & \color{red}{-550x} +33 \\\Leftrightarrow & -440x \color{red}{-100} \color{blue}{+100} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{+100} \\\Leftrightarrow & -440x+550x& = & 33+100 \\\Leftrightarrow & \color{red}{110} x& = & 133 \\\Leftrightarrow & x = \frac{133}{110} & & \\ & V = \left\{ \frac{133}{110} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{4})& = & -5x+\frac{10}{9} \\\Leftrightarrow & -9x+\frac{9}{4}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-324}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -324x \color{red}{+81} & = & \color{red}{-180x} +40 \\\Leftrightarrow & -324x \color{red}{+81} \color{blue}{-81} \color{blue}{+180x} & = & \color{red}{-180x} +40 \color{blue}{+180x} \color{blue}{-81} \\\Leftrightarrow & -324x+180x& = & 40-81 \\\Leftrightarrow & \color{red}{-144} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-144} & & \\\Leftrightarrow & x = \frac{41}{144} & & \\ & V = \left\{ \frac{41}{144} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{2})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 28x-\frac{21}{2}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{280}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 280x \color{red}{-105} & = & \color{red}{90x} +16 \\\Leftrightarrow & 280x \color{red}{-105} \color{blue}{+105} \color{blue}{-90x} & = & \color{red}{90x} +16 \color{blue}{-90x} \color{blue}{+105} \\\Leftrightarrow & 280x-90x& = & 16+105 \\\Leftrightarrow & \color{red}{190} x& = & 121 \\\Leftrightarrow & x = \frac{121}{190} & & \\ & V = \left\{ \frac{121}{190} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-180} & = & \color{red}{567x} +70 \\\Leftrightarrow & 1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{+180} \\\Leftrightarrow & 1260x-567x& = & 70+180 \\\Leftrightarrow & \color{red}{693} x& = & 250 \\\Leftrightarrow & x = \frac{250}{693} & & \\ & V = \left\{ \frac{250}{693} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-630}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{50}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -630x \color{red}{-63} & = & \color{red}{-490x} +50 \\\Leftrightarrow & -630x \color{red}{-63} \color{blue}{+63} \color{blue}{+490x} & = & \color{red}{-490x} +50 \color{blue}{+490x} \color{blue}{+63} \\\Leftrightarrow & -630x+490x& = & 50+63 \\\Leftrightarrow & \color{red}{-140} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-140} & & \\\Leftrightarrow & x = \frac{-113}{140} & & \\ & V = \left\{ \frac{-113}{140} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & -3x+\frac{5}{3} \\\Leftrightarrow & -14x-\frac{35}{9}& = & -3x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x- \frac{35}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{-35} & = & \color{red}{-27x} +15 \\\Leftrightarrow & -126x \color{red}{-35} \color{blue}{+35} \color{blue}{+27x} & = & \color{red}{-27x} +15 \color{blue}{+27x} \color{blue}{+35} \\\Leftrightarrow & -126x+27x& = & 15+35 \\\Leftrightarrow & \color{red}{-99} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-99} & & \\\Leftrightarrow & x = \frac{-50}{99} & & \\ & V = \left\{ \frac{-50}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-420}{ \color{blue}{42} }x+ \frac{36}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -420x \color{red}{+36} & = & \color{red}{294x} +35 \\\Leftrightarrow & -420x \color{red}{+36} \color{blue}{-36} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{-36} \\\Leftrightarrow & -420x-294x& = & 35-36 \\\Leftrightarrow & \color{red}{-714} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-714} & & \\\Leftrightarrow & x = \frac{1}{714} & & \\ & V = \left\{ \frac{1}{714} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-210} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 924x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 924x+385x& = & 22+210 \\\Leftrightarrow & \color{red}{1309} x& = & 232 \\\Leftrightarrow & x = \frac{232}{1309} & & \\ & V = \left\{ \frac{232}{1309} \right\} & \\\end{align}\)
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