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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{11})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -30x+\frac{24}{11}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3960}{ \color{blue}{132} }x+ \frac{288}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3960x \color{red}{+288} & = & \color{red}{-924x} +77 \\\Leftrightarrow & -3960x \color{red}{+288} \color{blue}{-288} \color{blue}{+924x} & = & \color{red}{-924x} +77 \color{blue}{+924x} \color{blue}{-288} \\\Leftrightarrow & -3960x+924x& = & 77-288 \\\Leftrightarrow & \color{red}{-3036} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{-3036} & & \\\Leftrightarrow & x = \frac{211}{3036} & & \\ & V = \left\{ \frac{211}{3036} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-448}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -448x \color{red}{+64} & = & \color{red}{196x} +35 \\\Leftrightarrow & -448x \color{red}{+64} \color{blue}{-64} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-64} \\\Leftrightarrow & -448x-196x& = & 35-64 \\\Leftrightarrow & \color{red}{-644} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-644} & & \\\Leftrightarrow & x = \frac{29}{644} & & \\ & V = \left\{ \frac{29}{644} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{81x} +30 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +30 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -72x-81x& = & 30-8 \\\Leftrightarrow & \color{red}{-153} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-153} & & \\\Leftrightarrow & x = \frac{-22}{153} & & \\ & V = \left\{ \frac{-22}{153} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{4}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+16} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -264x \color{red}{+16} \color{blue}{-16} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{-16} \\\Leftrightarrow & -264x+308x& = & 33-16 \\\Leftrightarrow & \color{red}{44} x& = & 17 \\\Leftrightarrow & x = \frac{17}{44} & & \\ & V = \left\{ \frac{17}{44} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 15x+\frac{20}{11}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1650}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1650x \color{red}{+200} & = & \color{red}{-770x} +77 \\\Leftrightarrow & 1650x \color{red}{+200} \color{blue}{-200} \color{blue}{+770x} & = & \color{red}{-770x} +77 \color{blue}{+770x} \color{blue}{-200} \\\Leftrightarrow & 1650x+770x& = & 77-200 \\\Leftrightarrow & \color{red}{2420} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{2420} & & \\ & V = \left\{ \frac{-123}{2420} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{16}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-48} & = & \color{red}{147x} +70 \\\Leftrightarrow & 420x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & 420x-147x& = & 70+48 \\\Leftrightarrow & \color{red}{273} x& = & 118 \\\Leftrightarrow & x = \frac{118}{273} & & \\ & V = \left\{ \frac{118}{273} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{11})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+72} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -792x \color{red}{+72} \color{blue}{-72} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-72} \\\Leftrightarrow & -792x+297x& = & 88-72 \\\Leftrightarrow & \color{red}{-495} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-495} & & \\\Leftrightarrow & x = \frac{-16}{495} & & \\ & V = \left\{ \frac{-16}{495} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 30x-\frac{30}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x- \frac{270}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{-270} & = & \color{red}{-693x} +22 \\\Leftrightarrow & 2970x \color{red}{-270} \color{blue}{+270} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{+270} \\\Leftrightarrow & 2970x+693x& = & 22+270 \\\Leftrightarrow & \color{red}{3663} x& = & 292 \\\Leftrightarrow & x = \frac{292}{3663} & & \\ & V = \left\{ \frac{292}{3663} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{3}{8} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-64}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -168x \color{red}{-21} & = & \color{red}{-64x} +3 \\\Leftrightarrow & -168x \color{red}{-21} \color{blue}{+21} \color{blue}{+64x} & = & \color{red}{-64x} +3 \color{blue}{+64x} \color{blue}{+21} \\\Leftrightarrow & -168x+64x& = & 3+21 \\\Leftrightarrow & \color{red}{-104} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-104} & & \\\Leftrightarrow & x = \frac{-3}{13} & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{175x} +42 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & -315x-175x& = & 42+30 \\\Leftrightarrow & \color{red}{-490} x& = & 72 \\\Leftrightarrow & x = \frac{72}{-490} & & \\\Leftrightarrow & x = \frac{-36}{245} & & \\ & V = \left\{ \frac{-36}{245} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{70x} +35 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{-70x} & = & \color{red}{70x} +35 \color{blue}{-70x} \color{blue}{+8} \\\Leftrightarrow & -60x-70x& = & 35+8 \\\Leftrightarrow & \color{red}{-130} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-130} & & \\\Leftrightarrow & x = \frac{-43}{130} & & \\ & V = \left\{ \frac{-43}{130} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & 2x+\frac{7}{2} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 2x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{20x} +35 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{-20x} & = & \color{red}{20x} +35 \color{blue}{-20x} \color{blue}{+24} \\\Leftrightarrow & 90x-20x& = & 35+24 \\\Leftrightarrow & \color{red}{70} x& = & 59 \\\Leftrightarrow & x = \frac{59}{70} & & \\ & V = \left\{ \frac{59}{70} \right\} & \\\end{align}\)
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