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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{8}{9}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+88} & = & \color{red}{-495x} +90 \\\Leftrightarrow & -1188x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +90 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & -1188x+495x& = & 90-88 \\\Leftrightarrow & \color{red}{-693} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-693} & & \\\Leftrightarrow & x = \frac{-2}{693} & & \\ & V = \left\{ \frac{-2}{693} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-720}{ \color{blue}{72} }x- \frac{135}{ \color{blue}{72} })& = & (\frac{-504}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -720x \color{red}{-135} & = & \color{red}{-504x} +16 \\\Leftrightarrow & -720x \color{red}{-135} \color{blue}{+135} \color{blue}{+504x} & = & \color{red}{-504x} +16 \color{blue}{+504x} \color{blue}{+135} \\\Leftrightarrow & -720x+504x& = & 16+135 \\\Leftrightarrow & \color{red}{-216} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-216} & & \\\Leftrightarrow & x = \frac{-151}{216} & & \\ & V = \left\{ \frac{-151}{216} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{11})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -6x+\frac{9}{11}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+36} & = & \color{red}{308x} +33 \\\Leftrightarrow & -264x \color{red}{+36} \color{blue}{-36} \color{blue}{-308x} & = & \color{red}{308x} +33 \color{blue}{-308x} \color{blue}{-36} \\\Leftrightarrow & -264x-308x& = & 33-36 \\\Leftrightarrow & \color{red}{-572} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-572} & & \\\Leftrightarrow & x = \frac{3}{572} & & \\ & V = \left\{ \frac{3}{572} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+42} & = & \color{red}{-245x} +50 \\\Leftrightarrow & -210x \color{red}{+42} \color{blue}{-42} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-42} \\\Leftrightarrow & -210x+245x& = & 50-42 \\\Leftrightarrow & \color{red}{35} x& = & 8 \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{9})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{9}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{630}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 630x \color{red}{-175} & = & \color{red}{-135x} +54 \\\Leftrightarrow & 630x \color{red}{-175} \color{blue}{+175} \color{blue}{+135x} & = & \color{red}{-135x} +54 \color{blue}{+135x} \color{blue}{+175} \\\Leftrightarrow & 630x+135x& = & 54+175 \\\Leftrightarrow & \color{red}{765} x& = & 229 \\\Leftrightarrow & x = \frac{229}{765} & & \\ & V = \left\{ \frac{229}{765} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{120x} +64 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{-120x} & = & \color{red}{120x} +64 \color{blue}{-120x} \color{blue}{-63} \\\Leftrightarrow & -336x-120x& = & 64-63 \\\Leftrightarrow & \color{red}{-456} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-456} & & \\\Leftrightarrow & x = \frac{-1}{456} & & \\ & V = \left\{ \frac{-1}{456} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{6})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+105} & = & \color{red}{-90x} +16 \\\Leftrightarrow & -504x \color{red}{+105} \color{blue}{-105} \color{blue}{+90x} & = & \color{red}{-90x} +16 \color{blue}{+90x} \color{blue}{-105} \\\Leftrightarrow & -504x+90x& = & 16-105 \\\Leftrightarrow & \color{red}{-414} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-414} & & \\\Leftrightarrow & x = \frac{89}{414} & & \\ & V = \left\{ \frac{89}{414} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{9})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-110} & = & \color{red}{-693x} +90 \\\Leftrightarrow & -990x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +90 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -990x+693x& = & 90+110 \\\Leftrightarrow & \color{red}{-297} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-297} & & \\\Leftrightarrow & x = \frac{-200}{297} & & \\ & V = \left\{ \frac{-200}{297} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{315x} +10 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & -280x-315x& = & 10+84 \\\Leftrightarrow & \color{red}{-595} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-595} & & \\\Leftrightarrow & x = \frac{-94}{595} & & \\ & V = \left\{ \frac{-94}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{-30} & = & \color{red}{-175x} +28 \\\Leftrightarrow & -140x \color{red}{-30} \color{blue}{+30} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{+30} \\\Leftrightarrow & -140x+175x& = & 28+30 \\\Leftrightarrow & \color{red}{35} x& = & 58 \\\Leftrightarrow & x = \frac{58}{35} & & \\ & V = \left\{ \frac{58}{35} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 4x+\frac{2}{11} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 4x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+154} & = & \color{red}{132x} +6 \\\Leftrightarrow & 1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-132x} & = & \color{red}{132x} +6 \color{blue}{-132x} \color{blue}{-154} \\\Leftrightarrow & 1155x-132x& = & 6-154 \\\Leftrightarrow & \color{red}{1023} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{1023} & & \\ & V = \left\{ \frac{-148}{1023} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -4x+\frac{7}{8} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -4x+\frac{7}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-21} & = & \color{red}{-32x} +7 \\\Leftrightarrow & -224x \color{red}{-21} \color{blue}{+21} \color{blue}{+32x} & = & \color{red}{-32x} +7 \color{blue}{+32x} \color{blue}{+21} \\\Leftrightarrow & -224x+32x& = & 7+21 \\\Leftrightarrow & \color{red}{-192} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-192} & & \\\Leftrightarrow & x = \frac{-7}{48} & & \\ & V = \left\{ \frac{-7}{48} \right\} & \\\end{align}\)
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