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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{11})& = & -9x+\frac{9}{8} \\\Leftrightarrow & -8x+\frac{12}{11}& = & -9x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-704}{ \color{blue}{88} }x+ \frac{96}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -704x \color{red}{+96} & = & \color{red}{-792x} +99 \\\Leftrightarrow & -704x \color{red}{+96} \color{blue}{-96} \color{blue}{+792x} & = & \color{red}{-792x} +99 \color{blue}{+792x} \color{blue}{-96} \\\Leftrightarrow & -704x+792x& = & 99-96 \\\Leftrightarrow & \color{red}{88} x& = & 3 \\\Leftrightarrow & x = \frac{3}{88} & & \\ & V = \left\{ \frac{3}{88} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 10x-\frac{20}{9}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{720}{ \color{blue}{72} }x- \frac{160}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{45}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 720x \color{red}{-160} & = & \color{red}{504x} +45 \\\Leftrightarrow & 720x \color{red}{-160} \color{blue}{+160} \color{blue}{-504x} & = & \color{red}{504x} +45 \color{blue}{-504x} \color{blue}{+160} \\\Leftrightarrow & 720x-504x& = & 45+160 \\\Leftrightarrow & \color{red}{216} x& = & 205 \\\Leftrightarrow & x = \frac{205}{216} & & \\ & V = \left\{ \frac{205}{216} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -18x+\frac{24}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+168} & = & \color{red}{105x} +45 \\\Leftrightarrow & -630x \color{red}{+168} \color{blue}{-168} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{-168} \\\Leftrightarrow & -630x-105x& = & 45-168 \\\Leftrightarrow & \color{red}{-735} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-735} & & \\\Leftrightarrow & x = \frac{41}{245} & & \\ & V = \left\{ \frac{41}{245} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+42} & = & \color{red}{-81x} +4 \\\Leftrightarrow & 252x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +4 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & 252x+81x& = & 4-42 \\\Leftrightarrow & \color{red}{333} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{333} & & \\ & V = \left\{ \frac{-38}{333} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 8x-\frac{16}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-80} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 440x \color{red}{-80} \color{blue}{+80} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+80} \\\Leftrightarrow & 440x+385x& = & 22+80 \\\Leftrightarrow & \color{red}{825} x& = & 102 \\\Leftrightarrow & x = \frac{102}{825} & & \\\Leftrightarrow & x = \frac{34}{275} & & \\ & V = \left\{ \frac{34}{275} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+16} & = & \color{red}{-18x} +27 \\\Leftrightarrow & -120x \color{red}{+16} \color{blue}{-16} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{-16} \\\Leftrightarrow & -120x+18x& = & 27-16 \\\Leftrightarrow & \color{red}{-102} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-102} & & \\\Leftrightarrow & x = \frac{-11}{102} & & \\ & V = \left\{ \frac{-11}{102} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+28} & = & \color{red}{-315x} +50 \\\Leftrightarrow & 280x \color{red}{+28} \color{blue}{-28} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{-28} \\\Leftrightarrow & 280x+315x& = & 50-28 \\\Leftrightarrow & \color{red}{595} x& = & 22 \\\Leftrightarrow & x = \frac{22}{595} & & \\ & V = \left\{ \frac{22}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{6}{7}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+30} & = & \color{red}{-140x} +42 \\\Leftrightarrow & -525x \color{red}{+30} \color{blue}{-30} \color{blue}{+140x} & = & \color{red}{-140x} +42 \color{blue}{+140x} \color{blue}{-30} \\\Leftrightarrow & -525x+140x& = & 42-30 \\\Leftrightarrow & \color{red}{-385} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-385} & & \\\Leftrightarrow & x = \frac{-12}{385} & & \\ & V = \left\{ \frac{-12}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{3})& = & -6x+\frac{5}{8} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -6x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{112}{ \color{blue}{24} })& = & (\frac{-144}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-112} & = & \color{red}{-144x} +15 \\\Leftrightarrow & -840x \color{red}{-112} \color{blue}{+112} \color{blue}{+144x} & = & \color{red}{-144x} +15 \color{blue}{+144x} \color{blue}{+112} \\\Leftrightarrow & -840x+144x& = & 15+112 \\\Leftrightarrow & \color{red}{-696} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-696} & & \\\Leftrightarrow & x = \frac{-127}{696} & & \\ & V = \left\{ \frac{-127}{696} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{7})& = & 2x+\frac{8}{5} \\\Leftrightarrow & 9x+\frac{9}{7}& = & 2x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+45} & = & \color{red}{70x} +56 \\\Leftrightarrow & 315x \color{red}{+45} \color{blue}{-45} \color{blue}{-70x} & = & \color{red}{70x} +56 \color{blue}{-70x} \color{blue}{-45} \\\Leftrightarrow & 315x-70x& = & 56-45 \\\Leftrightarrow & \color{red}{245} x& = & 11 \\\Leftrightarrow & x = \frac{11}{245} & & \\ & V = \left\{ \frac{11}{245} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{1}{2})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{7}{2}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{21}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-21} & = & \color{red}{18x} +8 \\\Leftrightarrow & -210x \color{red}{-21} \color{blue}{+21} \color{blue}{-18x} & = & \color{red}{18x} +8 \color{blue}{-18x} \color{blue}{+21} \\\Leftrightarrow & -210x-18x& = & 8+21 \\\Leftrightarrow & \color{red}{-228} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-228} & & \\\Leftrightarrow & x = \frac{-29}{228} & & \\ & V = \left\{ \frac{-29}{228} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{9})& = & -8x+\frac{10}{9} \\\Leftrightarrow & -21x-\frac{14}{9}& = & -8x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{14}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-14} & = & \color{red}{-72x} +10 \\\Leftrightarrow & -189x \color{red}{-14} \color{blue}{+14} \color{blue}{+72x} & = & \color{red}{-72x} +10 \color{blue}{+72x} \color{blue}{+14} \\\Leftrightarrow & -189x+72x& = & 10+14 \\\Leftrightarrow & \color{red}{-117} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-117} & & \\\Leftrightarrow & x = \frac{-8}{39} & & \\ & V = \left\{ \frac{-8}{39} \right\} & \\\end{align}\)
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