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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{2}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{175x} +49 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & 210x-175x& = & 49+30 \\\Leftrightarrow & \color{red}{35} x& = & 79 \\\Leftrightarrow & x = \frac{79}{35} & & \\ & V = \left\{ \frac{79}{35} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{5})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{6}{5}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{70x} +45 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +45 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -60x-70x& = & 45-12 \\\Leftrightarrow & \color{red}{-130} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-130} & & \\\Leftrightarrow & x = \frac{-33}{130} & & \\ & V = \left\{ \frac{-33}{130} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & 8x+\frac{3}{10} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{+105} & = & \color{red}{320x} +12 \\\Leftrightarrow & -840x \color{red}{+105} \color{blue}{-105} \color{blue}{-320x} & = & \color{red}{320x} +12 \color{blue}{-320x} \color{blue}{-105} \\\Leftrightarrow & -840x-320x& = & 12-105 \\\Leftrightarrow & \color{red}{-1160} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-1160} & & \\\Leftrightarrow & x = \frac{93}{1160} & & \\ & V = \left\{ \frac{93}{1160} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & -4x+\frac{3}{8} \\\Leftrightarrow & 35x-\frac{21}{11}& = & -4x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{3080}{ \color{blue}{88} }x- \frac{168}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 3080x \color{red}{-168} & = & \color{red}{-352x} +33 \\\Leftrightarrow & 3080x \color{red}{-168} \color{blue}{+168} \color{blue}{+352x} & = & \color{red}{-352x} +33 \color{blue}{+352x} \color{blue}{+168} \\\Leftrightarrow & 3080x+352x& = & 33+168 \\\Leftrightarrow & \color{red}{3432} x& = & 201 \\\Leftrightarrow & x = \frac{201}{3432} & & \\\Leftrightarrow & x = \frac{67}{1144} & & \\ & V = \left\{ \frac{67}{1144} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -2x+\frac{8}{5} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -2x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{-40x} +32 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{+40x} & = & \color{red}{-40x} +32 \color{blue}{+40x} \color{blue}{+75} \\\Leftrightarrow & 500x+40x& = & 32+75 \\\Leftrightarrow & \color{red}{540} x& = & 107 \\\Leftrightarrow & x = \frac{107}{540} & & \\ & V = \left\{ \frac{107}{540} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 10x-\frac{8}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{64}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-64} & = & \color{red}{616x} +77 \\\Leftrightarrow & 880x \color{red}{-64} \color{blue}{+64} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{+64} \\\Leftrightarrow & 880x-616x& = & 77+64 \\\Leftrightarrow & \color{red}{264} x& = & 141 \\\Leftrightarrow & x = \frac{141}{264} & & \\\Leftrightarrow & x = \frac{47}{88} & & \\ & V = \left\{ \frac{47}{88} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -10x+\frac{8}{3}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+56} & = & \color{red}{147x} +6 \\\Leftrightarrow & -210x \color{red}{+56} \color{blue}{-56} \color{blue}{-147x} & = & \color{red}{147x} +6 \color{blue}{-147x} \color{blue}{-56} \\\Leftrightarrow & -210x-147x& = & 6-56 \\\Leftrightarrow & \color{red}{-357} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-357} & & \\\Leftrightarrow & x = \frac{50}{357} & & \\ & V = \left\{ \frac{50}{357} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{4}{3}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-28} & = & \color{red}{-105x} +24 \\\Leftrightarrow & 168x \color{red}{-28} \color{blue}{+28} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{+28} \\\Leftrightarrow & 168x+105x& = & 24+28 \\\Leftrightarrow & \color{red}{273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{273} & & \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 180x+63x& = & 30-8 \\\Leftrightarrow & \color{red}{243} x& = & 22 \\\Leftrightarrow & x = \frac{22}{243} & & \\ & V = \left\{ \frac{22}{243} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+50} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 150x \color{red}{+50} \color{blue}{-50} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-50} \\\Leftrightarrow & 150x+105x& = & 18-50 \\\Leftrightarrow & \color{red}{255} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{255} & & \\ & V = \left\{ \frac{-32}{255} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 16x-\frac{16}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{224}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 224x \color{red}{-32} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 224x \color{red}{-32} \color{blue}{+32} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+32} \\\Leftrightarrow & 224x+70x& = & 35+32 \\\Leftrightarrow & \color{red}{294} x& = & 67 \\\Leftrightarrow & x = \frac{67}{294} & & \\ & V = \left\{ \frac{67}{294} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+14} & = & \color{red}{9x} +2 \\\Leftrightarrow & 84x \color{red}{+14} \color{blue}{-14} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-14} \\\Leftrightarrow & 84x-9x& = & 2-14 \\\Leftrightarrow & \color{red}{75} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{75} & & \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
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