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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{5})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 16x+\frac{8}{5}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{+16} & = & \color{red}{30x} +35 \\\Leftrightarrow & 160x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +35 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & 160x-30x& = & 35-16 \\\Leftrightarrow & \color{red}{130} x& = & 19 \\\Leftrightarrow & x = \frac{19}{130} & & \\ & V = \left\{ \frac{19}{130} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{8})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{15}{8}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-105} & = & \color{red}{-280x} +80 \\\Leftrightarrow & 672x \color{red}{-105} \color{blue}{+105} \color{blue}{+280x} & = & \color{red}{-280x} +80 \color{blue}{+280x} \color{blue}{+105} \\\Leftrightarrow & 672x+280x& = & 80+105 \\\Leftrightarrow & \color{red}{952} x& = & 185 \\\Leftrightarrow & x = \frac{185}{952} & & \\ & V = \left\{ \frac{185}{952} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-175}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+10} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -175x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & -175x+63x& = & 4-10 \\\Leftrightarrow & \color{red}{-112} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-112} & & \\\Leftrightarrow & x = \frac{3}{56} & & \\ & V = \left\{ \frac{3}{56} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{-49x} +8 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -42x+49x& = & 8-6 \\\Leftrightarrow & \color{red}{7} x& = & 2 \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{3}{8})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{+189} & = & \color{red}{216x} +80 \\\Leftrightarrow & -1008x \color{red}{+189} \color{blue}{-189} \color{blue}{-216x} & = & \color{red}{216x} +80 \color{blue}{-216x} \color{blue}{-189} \\\Leftrightarrow & -1008x-216x& = & 80-189 \\\Leftrightarrow & \color{red}{-1224} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-1224} & & \\\Leftrightarrow & x = \frac{109}{1224} & & \\ & V = \left\{ \frac{109}{1224} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{+147} & = & \color{red}{-504x} +80 \\\Leftrightarrow & -1960x \color{red}{+147} \color{blue}{-147} \color{blue}{+504x} & = & \color{red}{-504x} +80 \color{blue}{+504x} \color{blue}{-147} \\\Leftrightarrow & -1960x+504x& = & 80-147 \\\Leftrightarrow & \color{red}{-1456} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1456} & & \\\Leftrightarrow & x = \frac{67}{1456} & & \\ & V = \left\{ \frac{67}{1456} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{539x} +21 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & 770x-539x& = & 21+110 \\\Leftrightarrow & \color{red}{231} x& = & 131 \\\Leftrightarrow & x = \frac{131}{231} & & \\ & V = \left\{ \frac{131}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-66} & = & \color{red}{-231x} +28 \\\Leftrightarrow & 616x \color{red}{-66} \color{blue}{+66} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{+66} \\\Leftrightarrow & 616x+231x& = & 28+66 \\\Leftrightarrow & \color{red}{847} x& = & 94 \\\Leftrightarrow & x = \frac{94}{847} & & \\ & V = \left\{ \frac{94}{847} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{3})& = & -2x+\frac{4}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -2x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{-66x} +12 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{+66x} & = & \color{red}{-66x} +12 \color{blue}{+66x} \color{blue}{+154} \\\Leftrightarrow & 693x+66x& = & 12+154 \\\Leftrightarrow & \color{red}{759} x& = & 166 \\\Leftrightarrow & x = \frac{166}{759} & & \\ & V = \left\{ \frac{166}{759} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-12} & = & \color{red}{-33x} +6 \\\Leftrightarrow & -88x \color{red}{-12} \color{blue}{+12} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+12} \\\Leftrightarrow & -88x+33x& = & 6+12 \\\Leftrightarrow & \color{red}{-55} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-55} & & \\\Leftrightarrow & x = \frac{-18}{55} & & \\ & V = \left\{ \frac{-18}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x- \frac{60}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{-60} & = & \color{red}{378x} +35 \\\Leftrightarrow & 840x \color{red}{-60} \color{blue}{+60} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{+60} \\\Leftrightarrow & 840x-378x& = & 35+60 \\\Leftrightarrow & \color{red}{462} x& = & 95 \\\Leftrightarrow & x = \frac{95}{462} & & \\ & V = \left\{ \frac{95}{462} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{-40} & = & \color{red}{315x} +18 \\\Leftrightarrow & -450x \color{red}{-40} \color{blue}{+40} \color{blue}{-315x} & = & \color{red}{315x} +18 \color{blue}{-315x} \color{blue}{+40} \\\Leftrightarrow & -450x-315x& = & 18+40 \\\Leftrightarrow & \color{red}{-765} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-765} & & \\\Leftrightarrow & x = \frac{-58}{765} & & \\ & V = \left\{ \frac{-58}{765} \right\} & \\\end{align}\)
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