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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{9})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{432}{ \color{blue}{72} }x- \frac{64}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 432x \color{red}{-64} & = & \color{red}{-360x} +81 \\\Leftrightarrow & 432x \color{red}{-64} \color{blue}{+64} \color{blue}{+360x} & = & \color{red}{-360x} +81 \color{blue}{+360x} \color{blue}{+64} \\\Leftrightarrow & 432x+360x& = & 81+64 \\\Leftrightarrow & \color{red}{792} x& = & 145 \\\Leftrightarrow & x = \frac{145}{792} & & \\ & V = \left\{ \frac{145}{792} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{8})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{+21} & = & \color{red}{72x} +36 \\\Leftrightarrow & -280x \color{red}{+21} \color{blue}{-21} \color{blue}{-72x} & = & \color{red}{72x} +36 \color{blue}{-72x} \color{blue}{-21} \\\Leftrightarrow & -280x-72x& = & 36-21 \\\Leftrightarrow & \color{red}{-352} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-352} & & \\\Leftrightarrow & x = \frac{-15}{352} & & \\ & V = \left\{ \frac{-15}{352} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-90} & = & \color{red}{385x} +44 \\\Leftrightarrow & -1650x \color{red}{-90} \color{blue}{+90} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+90} \\\Leftrightarrow & -1650x-385x& = & 44+90 \\\Leftrightarrow & \color{red}{-2035} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-2035} & & \\\Leftrightarrow & x = \frac{-134}{2035} & & \\ & V = \left\{ \frac{-134}{2035} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{11})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{10}{11}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{-10} & = & \color{red}{55x} +6 \\\Leftrightarrow & 66x \color{red}{-10} \color{blue}{+10} \color{blue}{-55x} & = & \color{red}{55x} +6 \color{blue}{-55x} \color{blue}{+10} \\\Leftrightarrow & 66x-55x& = & 6+10 \\\Leftrightarrow & \color{red}{11} x& = & 16 \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{4})& = & 6x+\frac{8}{5} \\\Leftrightarrow & 35x-\frac{35}{4}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{700}{ \color{blue}{20} }x- \frac{175}{ \color{blue}{20} })& = & (\frac{120}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 700x \color{red}{-175} & = & \color{red}{120x} +32 \\\Leftrightarrow & 700x \color{red}{-175} \color{blue}{+175} \color{blue}{-120x} & = & \color{red}{120x} +32 \color{blue}{-120x} \color{blue}{+175} \\\Leftrightarrow & 700x-120x& = & 32+175 \\\Leftrightarrow & \color{red}{580} x& = & 207 \\\Leftrightarrow & x = \frac{207}{580} & & \\ & V = \left\{ \frac{207}{580} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -8x+\frac{7}{6} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -8x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-540}{ \color{blue}{30} }x+ \frac{144}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -540x \color{red}{+144} & = & \color{red}{-240x} +35 \\\Leftrightarrow & -540x \color{red}{+144} \color{blue}{-144} \color{blue}{+240x} & = & \color{red}{-240x} +35 \color{blue}{+240x} \color{blue}{-144} \\\Leftrightarrow & -540x+240x& = & 35-144 \\\Leftrightarrow & \color{red}{-300} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-300} & & \\\Leftrightarrow & x = \frac{109}{300} & & \\ & V = \left\{ \frac{109}{300} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{-8} & = & \color{red}{21x} +8 \\\Leftrightarrow & -18x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & -18x-21x& = & 8+8 \\\Leftrightarrow & \color{red}{-39} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-39} & & \\\Leftrightarrow & x = \frac{-16}{39} & & \\ & V = \left\{ \frac{-16}{39} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{10})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -14x-\frac{21}{10}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x- \frac{21}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{-21} & = & \color{red}{-30x} +16 \\\Leftrightarrow & -140x \color{red}{-21} \color{blue}{+21} \color{blue}{+30x} & = & \color{red}{-30x} +16 \color{blue}{+30x} \color{blue}{+21} \\\Leftrightarrow & -140x+30x& = & 16+21 \\\Leftrightarrow & \color{red}{-110} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-110} & & \\\Leftrightarrow & x = \frac{-37}{110} & & \\ & V = \left\{ \frac{-37}{110} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{28}{9}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+28} & = & \color{red}{-72x} +24 \\\Leftrightarrow & 189x \color{red}{+28} \color{blue}{-28} \color{blue}{+72x} & = & \color{red}{-72x} +24 \color{blue}{+72x} \color{blue}{-28} \\\Leftrightarrow & 189x+72x& = & 24-28 \\\Leftrightarrow & \color{red}{261} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{261} & & \\ & V = \left\{ \frac{-4}{261} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+28} & = & \color{red}{245x} +50 \\\Leftrightarrow & -350x \color{red}{+28} \color{blue}{-28} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-28} \\\Leftrightarrow & -350x-245x& = & 50-28 \\\Leftrightarrow & \color{red}{-595} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-595} & & \\\Leftrightarrow & x = \frac{-22}{595} & & \\ & V = \left\{ \frac{-22}{595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{7})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -10x-\frac{8}{7}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x- \frac{32}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{-32} & = & \color{red}{-196x} +35 \\\Leftrightarrow & -280x \color{red}{-32} \color{blue}{+32} \color{blue}{+196x} & = & \color{red}{-196x} +35 \color{blue}{+196x} \color{blue}{+32} \\\Leftrightarrow & -280x+196x& = & 35+32 \\\Leftrightarrow & \color{red}{-84} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-84} & & \\\Leftrightarrow & x = \frac{-67}{84} & & \\ & V = \left\{ \frac{-67}{84} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-132} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 924x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 924x+385x& = & 42+132 \\\Leftrightarrow & \color{red}{1309} x& = & 174 \\\Leftrightarrow & x = \frac{174}{1309} & & \\ & V = \left\{ \frac{174}{1309} \right\} & \\\end{align}\)
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