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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{3})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{8}{3}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-56} & = & \color{red}{-105x} +27 \\\Leftrightarrow & -252x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +27 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & -252x+105x& = & 27+56 \\\Leftrightarrow & \color{red}{-147} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-147} & & \\\Leftrightarrow & x = \frac{-83}{147} & & \\ & V = \left\{ \frac{-83}{147} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +40 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +40 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 40+84 \\\Leftrightarrow & \color{red}{-245} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-245} & & \\\Leftrightarrow & x = \frac{-124}{245} & & \\ & V = \left\{ \frac{-124}{245} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{175x} +30 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +30 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 420x-175x& = & 30+84 \\\Leftrightarrow & \color{red}{245} x& = & 114 \\\Leftrightarrow & x = \frac{114}{245} & & \\ & V = \left\{ \frac{114}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{3}{2})& = & 3x+\frac{5}{12} \\\Leftrightarrow & 28x+\frac{21}{2}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 2 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x+ \frac{126}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{+126} & = & \color{red}{36x} +5 \\\Leftrightarrow & 336x \color{red}{+126} \color{blue}{-126} \color{blue}{-36x} & = & \color{red}{36x} +5 \color{blue}{-36x} \color{blue}{-126} \\\Leftrightarrow & 336x-36x& = & 5-126 \\\Leftrightarrow & \color{red}{300} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{300} & & \\ & V = \left\{ \frac{-121}{300} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{7})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 8x-\frac{8}{7}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{560}{ \color{blue}{70} }x- \frac{80}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 560x \color{red}{-80} & = & \color{red}{-350x} +49 \\\Leftrightarrow & 560x \color{red}{-80} \color{blue}{+80} \color{blue}{+350x} & = & \color{red}{-350x} +49 \color{blue}{+350x} \color{blue}{+80} \\\Leftrightarrow & 560x+350x& = & 49+80 \\\Leftrightarrow & \color{red}{910} x& = & 129 \\\Leftrightarrow & x = \frac{129}{910} & & \\ & V = \left\{ \frac{129}{910} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -24x-\frac{24}{7}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{264}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-264} & = & \color{red}{-539x} +70 \\\Leftrightarrow & -1848x \color{red}{-264} \color{blue}{+264} \color{blue}{+539x} & = & \color{red}{-539x} +70 \color{blue}{+539x} \color{blue}{+264} \\\Leftrightarrow & -1848x+539x& = & 70+264 \\\Leftrightarrow & \color{red}{-1309} x& = & 334 \\\Leftrightarrow & x = \frac{334}{-1309} & & \\\Leftrightarrow & x = \frac{-334}{1309} & & \\ & V = \left\{ \frac{-334}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & -9x+\frac{6}{7} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{-189x} +18 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{+189x} & = & \color{red}{-189x} +18 \color{blue}{+189x} \color{blue}{-140} \\\Leftrightarrow & -420x+189x& = & 18-140 \\\Leftrightarrow & \color{red}{-231} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-231} & & \\\Leftrightarrow & x = \frac{122}{231} & & \\ & V = \left\{ \frac{122}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{6})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 20x+\frac{25}{6}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{54}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{+125} & = & \color{red}{-210x} +54 \\\Leftrightarrow & 600x \color{red}{+125} \color{blue}{-125} \color{blue}{+210x} & = & \color{red}{-210x} +54 \color{blue}{+210x} \color{blue}{-125} \\\Leftrightarrow & 600x+210x& = & 54-125 \\\Leftrightarrow & \color{red}{810} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{810} & & \\ & V = \left\{ \frac{-71}{810} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -6x+\frac{7}{12} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -6x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-72}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{-56} & = & \color{red}{-72x} +7 \\\Leftrightarrow & -420x \color{red}{-56} \color{blue}{+56} \color{blue}{+72x} & = & \color{red}{-72x} +7 \color{blue}{+72x} \color{blue}{+56} \\\Leftrightarrow & -420x+72x& = & 7+56 \\\Leftrightarrow & \color{red}{-348} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-348} & & \\\Leftrightarrow & x = \frac{-21}{116} & & \\ & V = \left\{ \frac{-21}{116} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{3}{11})& = & -3x+\frac{4}{7} \\\Leftrightarrow & 10x+\frac{15}{11}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+105} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 770x \color{red}{+105} \color{blue}{-105} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{-105} \\\Leftrightarrow & 770x+231x& = & 44-105 \\\Leftrightarrow & \color{red}{1001} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1001} & & \\ & V = \left\{ \frac{-61}{1001} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & -8x+\frac{7}{9} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+42} & = & \color{red}{-72x} +7 \\\Leftrightarrow & 189x \color{red}{+42} \color{blue}{-42} \color{blue}{+72x} & = & \color{red}{-72x} +7 \color{blue}{+72x} \color{blue}{-42} \\\Leftrightarrow & 189x+72x& = & 7-42 \\\Leftrightarrow & \color{red}{261} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{261} & & \\ & V = \left\{ \frac{-35}{261} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2112}{ \color{blue}{88} }x+ \frac{144}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2112x \color{red}{+144} & = & \color{red}{440x} +55 \\\Leftrightarrow & -2112x \color{red}{+144} \color{blue}{-144} \color{blue}{-440x} & = & \color{red}{440x} +55 \color{blue}{-440x} \color{blue}{-144} \\\Leftrightarrow & -2112x-440x& = & 55-144 \\\Leftrightarrow & \color{red}{-2552} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-2552} & & \\\Leftrightarrow & x = \frac{89}{2552} & & \\ & V = \left\{ \frac{89}{2552} \right\} & \\\end{align}\)
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