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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & -2x+\frac{7}{9} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+108} & = & \color{red}{-90x} +35 \\\Leftrightarrow & 675x \color{red}{+108} \color{blue}{-108} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{-108} \\\Leftrightarrow & 675x+90x& = & 35-108 \\\Leftrightarrow & \color{red}{765} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{765} & & \\ & V = \left\{ \frac{-73}{765} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{+84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -315x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & -315x+175x& = & 20-84 \\\Leftrightarrow & \color{red}{-140} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-140} & & \\\Leftrightarrow & x = \frac{16}{35} & & \\ & V = \left\{ \frac{16}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{11})& = & 8x+\frac{7}{9} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 8x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{135}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-135} & = & \color{red}{792x} +77 \\\Leftrightarrow & -1485x \color{red}{-135} \color{blue}{+135} \color{blue}{-792x} & = & \color{red}{792x} +77 \color{blue}{-792x} \color{blue}{+135} \\\Leftrightarrow & -1485x-792x& = & 77+135 \\\Leftrightarrow & \color{red}{-2277} x& = & 212 \\\Leftrightarrow & x = \frac{212}{-2277} & & \\\Leftrightarrow & x = \frac{-212}{2277} & & \\ & V = \left\{ \frac{-212}{2277} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{11})& = & -8x+\frac{7}{11} \\\Leftrightarrow & -21x+\frac{21}{11}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+21} & = & \color{red}{-88x} +7 \\\Leftrightarrow & -231x \color{red}{+21} \color{blue}{-21} \color{blue}{+88x} & = & \color{red}{-88x} +7 \color{blue}{+88x} \color{blue}{-21} \\\Leftrightarrow & -231x+88x& = & 7-21 \\\Leftrightarrow & \color{red}{-143} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-143} & & \\\Leftrightarrow & x = \frac{14}{143} & & \\ & V = \left\{ \frac{14}{143} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{6})& = & -9x+\frac{10}{7} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1176}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1176x \color{red}{+245} & = & \color{red}{-378x} +60 \\\Leftrightarrow & -1176x \color{red}{+245} \color{blue}{-245} \color{blue}{+378x} & = & \color{red}{-378x} +60 \color{blue}{+378x} \color{blue}{-245} \\\Leftrightarrow & -1176x+378x& = & 60-245 \\\Leftrightarrow & \color{red}{-798} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-798} & & \\\Leftrightarrow & x = \frac{185}{798} & & \\ & V = \left\{ \frac{185}{798} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{7})& = & -2x+\frac{4}{5} \\\Leftrightarrow & 25x-\frac{20}{7}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 875x \color{red}{-100} & = & \color{red}{-70x} +28 \\\Leftrightarrow & 875x \color{red}{-100} \color{blue}{+100} \color{blue}{+70x} & = & \color{red}{-70x} +28 \color{blue}{+70x} \color{blue}{+100} \\\Leftrightarrow & 875x+70x& = & 28+100 \\\Leftrightarrow & \color{red}{945} x& = & 128 \\\Leftrightarrow & x = \frac{128}{945} & & \\ & V = \left\{ \frac{128}{945} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{-189x} +9 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{+189x} & = & \color{red}{-189x} +9 \color{blue}{+189x} \color{blue}{-140} \\\Leftrightarrow & -168x+189x& = & 9-140 \\\Leftrightarrow & \color{red}{21} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{21} & & \\ & V = \left\{ \frac{-131}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x- \frac{200}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{-200} & = & \color{red}{810x} +27 \\\Leftrightarrow & -1800x \color{red}{-200} \color{blue}{+200} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{+200} \\\Leftrightarrow & -1800x-810x& = & 27+200 \\\Leftrightarrow & \color{red}{-2610} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-2610} & & \\\Leftrightarrow & x = \frac{-227}{2610} & & \\ & V = \left\{ \frac{-227}{2610} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-220} & = & \color{red}{-539x} +35 \\\Leftrightarrow & 1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & 1232x+539x& = & 35+220 \\\Leftrightarrow & \color{red}{1771} x& = & 255 \\\Leftrightarrow & x = \frac{255}{1771} & & \\ & V = \left\{ \frac{255}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{9})& = & -7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{8}{9}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-540}{ \color{blue}{90} }x+ \frac{80}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -540x \color{red}{+80} & = & \color{red}{-630x} +81 \\\Leftrightarrow & -540x \color{red}{+80} \color{blue}{-80} \color{blue}{+630x} & = & \color{red}{-630x} +81 \color{blue}{+630x} \color{blue}{-80} \\\Leftrightarrow & -540x+630x& = & 81-80 \\\Leftrightarrow & \color{red}{90} x& = & 1 \\\Leftrightarrow & x = \frac{1}{90} & & \\ & V = \left\{ \frac{1}{90} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -9x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-189x} +35 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +35 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & -168x+189x& = & 35-30 \\\Leftrightarrow & \color{red}{21} x& = & 5 \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{792}{ \color{blue}{66} }x- \frac{144}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 792x \color{red}{-144} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 792x \color{red}{-144} \color{blue}{+144} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+144} \\\Leftrightarrow & 792x+330x& = & 77+144 \\\Leftrightarrow & \color{red}{1122} x& = & 221 \\\Leftrightarrow & x = \frac{221}{1122} & & \\\Leftrightarrow & x = \frac{13}{66} & & \\ & V = \left\{ \frac{13}{66} \right\} & \\\end{align}\)
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