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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-88} & = & \color{red}{495x} +54 \\\Leftrightarrow & 396x \color{red}{-88} \color{blue}{+88} \color{blue}{-495x} & = & \color{red}{495x} +54 \color{blue}{-495x} \color{blue}{+88} \\\Leftrightarrow & 396x-495x& = & 54+88 \\\Leftrightarrow & \color{red}{-99} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-99} & & \\\Leftrightarrow & x = \frac{-142}{99} & & \\ & V = \left\{ \frac{-142}{99} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{9})& = & -3x+\frac{9}{8} \\\Leftrightarrow & 16x-\frac{20}{9}& = & -3x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1152}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1152x \color{red}{-160} & = & \color{red}{-216x} +81 \\\Leftrightarrow & 1152x \color{red}{-160} \color{blue}{+160} \color{blue}{+216x} & = & \color{red}{-216x} +81 \color{blue}{+216x} \color{blue}{+160} \\\Leftrightarrow & 1152x+216x& = & 81+160 \\\Leftrightarrow & \color{red}{1368} x& = & 241 \\\Leftrightarrow & x = \frac{241}{1368} & & \\ & V = \left\{ \frac{241}{1368} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{6})& = & -8x+\frac{2}{3} \\\Leftrightarrow & 21x-\frac{35}{6}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-35} & = & \color{red}{-48x} +4 \\\Leftrightarrow & 126x \color{red}{-35} \color{blue}{+35} \color{blue}{+48x} & = & \color{red}{-48x} +4 \color{blue}{+48x} \color{blue}{+35} \\\Leftrightarrow & 126x+48x& = & 4+35 \\\Leftrightarrow & \color{red}{174} x& = & 39 \\\Leftrightarrow & x = \frac{39}{174} & & \\\Leftrightarrow & x = \frac{13}{58} & & \\ & V = \left\{ \frac{13}{58} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -9x+\frac{9}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+99} & = & \color{red}{-275x} +50 \\\Leftrightarrow & -495x \color{red}{+99} \color{blue}{-99} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{-99} \\\Leftrightarrow & -495x+275x& = & 50-99 \\\Leftrightarrow & \color{red}{-220} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-220} & & \\\Leftrightarrow & x = \frac{49}{220} & & \\ & V = \left\{ \frac{49}{220} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{+72} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 1320x \color{red}{+72} \color{blue}{-72} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{-72} \\\Leftrightarrow & 1320x+308x& = & 99-72 \\\Leftrightarrow & \color{red}{1628} x& = & 27 \\\Leftrightarrow & x = \frac{27}{1628} & & \\ & V = \left\{ \frac{27}{1628} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{5})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 35x+\frac{21}{5}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x+ \frac{63}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{+63} & = & \color{red}{120x} +20 \\\Leftrightarrow & 525x \color{red}{+63} \color{blue}{-63} \color{blue}{-120x} & = & \color{red}{120x} +20 \color{blue}{-120x} \color{blue}{-63} \\\Leftrightarrow & 525x-120x& = & 20-63 \\\Leftrightarrow & \color{red}{405} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{405} & & \\ & V = \left\{ \frac{-43}{405} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1400}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1400x \color{red}{-100} & = & \color{red}{-490x} +21 \\\Leftrightarrow & -1400x \color{red}{-100} \color{blue}{+100} \color{blue}{+490x} & = & \color{red}{-490x} +21 \color{blue}{+490x} \color{blue}{+100} \\\Leftrightarrow & -1400x+490x& = & 21+100 \\\Leftrightarrow & \color{red}{-910} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-910} & & \\\Leftrightarrow & x = \frac{-121}{910} & & \\ & V = \left\{ \frac{-121}{910} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{7})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{8}{7}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x+ \frac{80}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{+80} & = & \color{red}{-490x} +63 \\\Leftrightarrow & -700x \color{red}{+80} \color{blue}{-80} \color{blue}{+490x} & = & \color{red}{-490x} +63 \color{blue}{+490x} \color{blue}{-80} \\\Leftrightarrow & -700x+490x& = & 63-80 \\\Leftrightarrow & \color{red}{-210} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-210} & & \\\Leftrightarrow & x = \frac{17}{210} & & \\ & V = \left\{ \frac{17}{210} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -4x+\frac{4}{3}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-132}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -132x \color{red}{+44} & = & \color{red}{-165x} +15 \\\Leftrightarrow & -132x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & -132x+165x& = & 15-44 \\\Leftrightarrow & \color{red}{33} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{33} & & \\ & V = \left\{ \frac{-29}{33} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{21x} +10 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -60x-21x& = & 10-8 \\\Leftrightarrow & \color{red}{-81} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-81} & & \\\Leftrightarrow & x = \frac{-2}{81} & & \\ & V = \left\{ \frac{-2}{81} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -18x+\frac{18}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1008}{ \color{blue}{56} }x+ \frac{144}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1008x \color{red}{+144} & = & \color{red}{280x} +49 \\\Leftrightarrow & -1008x \color{red}{+144} \color{blue}{-144} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{-144} \\\Leftrightarrow & -1008x-280x& = & 49-144 \\\Leftrightarrow & \color{red}{-1288} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-1288} & & \\\Leftrightarrow & x = \frac{95}{1288} & & \\ & V = \left\{ \frac{95}{1288} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-336}{ \color{blue}{56} }x- \frac{48}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{392x} +21 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-392x} & = & \color{red}{392x} +21 \color{blue}{-392x} \color{blue}{+48} \\\Leftrightarrow & -336x-392x& = & 21+48 \\\Leftrightarrow & \color{red}{-728} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-728} & & \\\Leftrightarrow & x = \frac{-69}{728} & & \\ & V = \left\{ \frac{-69}{728} \right\} & \\\end{align}\)
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