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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{11})& = & 5x+\frac{3}{11} \\\Leftrightarrow & -25x+\frac{25}{11}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{+25} & = & \color{red}{55x} +3 \\\Leftrightarrow & -275x \color{red}{+25} \color{blue}{-25} \color{blue}{-55x} & = & \color{red}{55x} +3 \color{blue}{-55x} \color{blue}{-25} \\\Leftrightarrow & -275x-55x& = & 3-25 \\\Leftrightarrow & \color{red}{-330} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-330} & & \\\Leftrightarrow & x = \frac{1}{15} & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{3})& = & -2x+\frac{9}{4} \\\Leftrightarrow & -25x+\frac{10}{3}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-300}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -300x \color{red}{+40} & = & \color{red}{-24x} +27 \\\Leftrightarrow & -300x \color{red}{+40} \color{blue}{-40} \color{blue}{+24x} & = & \color{red}{-24x} +27 \color{blue}{+24x} \color{blue}{-40} \\\Leftrightarrow & -300x+24x& = & 27-40 \\\Leftrightarrow & \color{red}{-276} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-276} & & \\\Leftrightarrow & x = \frac{13}{276} & & \\ & V = \left\{ \frac{13}{276} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{7})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{63x} +56 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{-63x} & = & \color{red}{63x} +56 \color{blue}{-63x} \color{blue}{-48} \\\Leftrightarrow & 336x-63x& = & 56-48 \\\Leftrightarrow & \color{red}{273} x& = & 8 \\\Leftrightarrow & x = \frac{8}{273} & & \\ & V = \left\{ \frac{8}{273} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-108} & = & \color{red}{315x} +50 \\\Leftrightarrow & 1350x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & 1350x-315x& = & 50+108 \\\Leftrightarrow & \color{red}{1035} x& = & 158 \\\Leftrightarrow & x = \frac{158}{1035} & & \\ & V = \left\{ \frac{158}{1035} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & -630x+441x& = & 49+90 \\\Leftrightarrow & \color{red}{-189} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-189} & & \\\Leftrightarrow & x = \frac{-139}{189} & & \\ & V = \left\{ \frac{-139}{189} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{3})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x+\frac{8}{3}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+40} & = & \color{red}{-105x} +12 \\\Leftrightarrow & -90x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +12 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & -90x+105x& = & 12-40 \\\Leftrightarrow & \color{red}{15} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{15} & & \\ & V = \left\{ \frac{-28}{15} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & 7x+\frac{9}{8} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{+48} & = & \color{red}{392x} +63 \\\Leftrightarrow & 560x \color{red}{+48} \color{blue}{-48} \color{blue}{-392x} & = & \color{red}{392x} +63 \color{blue}{-392x} \color{blue}{-48} \\\Leftrightarrow & 560x-392x& = & 63-48 \\\Leftrightarrow & \color{red}{168} x& = & 15 \\\Leftrightarrow & x = \frac{15}{168} & & \\\Leftrightarrow & x = \frac{5}{56} & & \\ & V = \left\{ \frac{5}{56} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{4}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-28} & = & \color{red}{441x} +90 \\\Leftrightarrow & -378x \color{red}{-28} \color{blue}{+28} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+28} \\\Leftrightarrow & -378x-441x& = & 90+28 \\\Leftrightarrow & \color{red}{-819} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-819} & & \\\Leftrightarrow & x = \frac{-118}{819} & & \\ & V = \left\{ \frac{-118}{819} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{5}{7})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{189x} +14 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{-189x} & = & \color{red}{189x} +14 \color{blue}{-189x} \color{blue}{+30} \\\Leftrightarrow & -168x-189x& = & 14+30 \\\Leftrightarrow & \color{red}{-357} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-357} & & \\\Leftrightarrow & x = \frac{-44}{357} & & \\ & V = \left\{ \frac{-44}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{24}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{264}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-264} & = & \color{red}{385x} +56 \\\Leftrightarrow & 924x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 924x-385x& = & 56+264 \\\Leftrightarrow & \color{red}{539} x& = & 320 \\\Leftrightarrow & x = \frac{320}{539} & & \\ & V = \left\{ \frac{320}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{4}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+36} & = & \color{red}{189x} +28 \\\Leftrightarrow & -504x \color{red}{+36} \color{blue}{-36} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{-36} \\\Leftrightarrow & -504x-189x& = & 28-36 \\\Leftrightarrow & \color{red}{-693} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-693} & & \\\Leftrightarrow & x = \frac{8}{693} & & \\ & V = \left\{ \frac{8}{693} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+30} & = & \color{red}{-189x} +70 \\\Leftrightarrow & -420x \color{red}{+30} \color{blue}{-30} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{-30} \\\Leftrightarrow & -420x+189x& = & 70-30 \\\Leftrightarrow & \color{red}{-231} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-231} & & \\\Leftrightarrow & x = \frac{-40}{231} & & \\ & V = \left\{ \frac{-40}{231} \right\} & \\\end{align}\)
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