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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -8x+\frac{10}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{-120x} +50 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{+120x} & = & \color{red}{-120x} +50 \color{blue}{+120x} \color{blue}{+36} \\\Leftrightarrow & 135x+120x& = & 50+36 \\\Leftrightarrow & \color{red}{255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{255} & & \\ & V = \left\{ \frac{86}{255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+270} & = & \color{red}{315x} +70 \\\Leftrightarrow & -756x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & -756x-315x& = & 70-270 \\\Leftrightarrow & \color{red}{-1071} x& = & -200 \\\Leftrightarrow & x = \frac{-200}{-1071} & & \\\Leftrightarrow & x = \frac{200}{1071} & & \\ & V = \left\{ \frac{200}{1071} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{-147x} +35 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +35 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & 168x+147x& = & 35-30 \\\Leftrightarrow & \color{red}{315} x& = & 5 \\\Leftrightarrow & x = \frac{5}{315} & & \\\Leftrightarrow & x = \frac{1}{63} & & \\ & V = \left\{ \frac{1}{63} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+24} & = & \color{red}{-63x} +2 \\\Leftrightarrow & 54x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & 54x+63x& = & 2-24 \\\Leftrightarrow & \color{red}{117} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{117} & & \\ & V = \left\{ \frac{-22}{117} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{11})& = & -6x+\frac{4}{11} \\\Leftrightarrow & -35x-\frac{21}{11}& = & -6x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-385}{ \color{blue}{11} }x- \frac{21}{ \color{blue}{11} })& = & (\frac{-66}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -385x \color{red}{-21} & = & \color{red}{-66x} +4 \\\Leftrightarrow & -385x \color{red}{-21} \color{blue}{+21} \color{blue}{+66x} & = & \color{red}{-66x} +4 \color{blue}{+66x} \color{blue}{+21} \\\Leftrightarrow & -385x+66x& = & 4+21 \\\Leftrightarrow & \color{red}{-319} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-319} & & \\\Leftrightarrow & x = \frac{-25}{319} & & \\ & V = \left\{ \frac{-25}{319} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -24x+\frac{30}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1584}{ \color{blue}{66} }x+ \frac{180}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1584x \color{red}{+180} & = & \color{red}{330x} +55 \\\Leftrightarrow & -1584x \color{red}{+180} \color{blue}{-180} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{-180} \\\Leftrightarrow & -1584x-330x& = & 55-180 \\\Leftrightarrow & \color{red}{-1914} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1914} & & \\\Leftrightarrow & x = \frac{125}{1914} & & \\ & V = \left\{ \frac{125}{1914} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{3})& = & -6x+\frac{10}{7} \\\Leftrightarrow & -35x+\frac{28}{3}& = & -6x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+196} & = & \color{red}{-126x} +30 \\\Leftrightarrow & -735x \color{red}{+196} \color{blue}{-196} \color{blue}{+126x} & = & \color{red}{-126x} +30 \color{blue}{+126x} \color{blue}{-196} \\\Leftrightarrow & -735x+126x& = & 30-196 \\\Leftrightarrow & \color{red}{-609} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-609} & & \\\Leftrightarrow & x = \frac{166}{609} & & \\ & V = \left\{ \frac{166}{609} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 3x+\frac{7}{4} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{+24} & = & \color{red}{132x} +77 \\\Leftrightarrow & 440x \color{red}{+24} \color{blue}{-24} \color{blue}{-132x} & = & \color{red}{132x} +77 \color{blue}{-132x} \color{blue}{-24} \\\Leftrightarrow & 440x-132x& = & 77-24 \\\Leftrightarrow & \color{red}{308} x& = & 53 \\\Leftrightarrow & x = \frac{53}{308} & & \\ & V = \left\{ \frac{53}{308} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{-56} & = & \color{red}{-108x} +27 \\\Leftrightarrow & 336x \color{red}{-56} \color{blue}{+56} \color{blue}{+108x} & = & \color{red}{-108x} +27 \color{blue}{+108x} \color{blue}{+56} \\\Leftrightarrow & 336x+108x& = & 27+56 \\\Leftrightarrow & \color{red}{444} x& = & 83 \\\Leftrightarrow & x = \frac{83}{444} & & \\ & V = \left\{ \frac{83}{444} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{4})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{15}{4}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 144x \color{red}{-45} & = & \color{red}{60x} +32 \\\Leftrightarrow & 144x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +32 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & 144x-60x& = & 32+45 \\\Leftrightarrow & \color{red}{84} x& = & 77 \\\Leftrightarrow & x = \frac{77}{84} & & \\\Leftrightarrow & x = \frac{11}{12} & & \\ & V = \left\{ \frac{11}{12} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-75}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -75x \color{red}{+20} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -75x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & -75x+21x& = & 2-20 \\\Leftrightarrow & \color{red}{-54} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-54} & & \\\Leftrightarrow & x = \frac{1}{3} & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x+\frac{6}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+42} & = & \color{red}{-175x} +45 \\\Leftrightarrow & -420x \color{red}{+42} \color{blue}{-42} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{-42} \\\Leftrightarrow & -420x+175x& = & 45-42 \\\Leftrightarrow & \color{red}{-245} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-245} & & \\\Leftrightarrow & x = \frac{-3}{245} & & \\ & V = \left\{ \frac{-3}{245} \right\} & \\\end{align}\)
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