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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 4x-\frac{8}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{176}{ \color{blue}{44} }x- \frac{32}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 176x \color{red}{-32} & = & \color{red}{308x} +99 \\\Leftrightarrow & 176x \color{red}{-32} \color{blue}{+32} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+32} \\\Leftrightarrow & 176x-308x& = & 99+32 \\\Leftrightarrow & \color{red}{-132} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-132} & & \\\Leftrightarrow & x = \frac{-131}{132} & & \\ & V = \left\{ \frac{-131}{132} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+24} \\\Leftrightarrow & -264x+55x& = & 2+24 \\\Leftrightarrow & \color{red}{-209} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-209} & & \\\Leftrightarrow & x = \frac{-26}{209} & & \\ & V = \left\{ \frac{-26}{209} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-44} & = & \color{red}{385x} +40 \\\Leftrightarrow & -330x \color{red}{-44} \color{blue}{+44} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+44} \\\Leftrightarrow & -330x-385x& = & 40+44 \\\Leftrightarrow & \color{red}{-715} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-715} & & \\\Leftrightarrow & x = \frac{-84}{715} & & \\ & V = \left\{ \frac{-84}{715} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & -7x+\frac{7}{10} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{300}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-300} & = & \color{red}{-770x} +77 \\\Leftrightarrow & 1320x \color{red}{-300} \color{blue}{+300} \color{blue}{+770x} & = & \color{red}{-770x} +77 \color{blue}{+770x} \color{blue}{+300} \\\Leftrightarrow & 1320x+770x& = & 77+300 \\\Leftrightarrow & \color{red}{2090} x& = & 377 \\\Leftrightarrow & x = \frac{377}{2090} & & \\ & V = \left\{ \frac{377}{2090} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 6x+\frac{3}{10} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 6x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{240}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{+105} & = & \color{red}{240x} +12 \\\Leftrightarrow & 1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-240x} & = & \color{red}{240x} +12 \color{blue}{-240x} \color{blue}{-105} \\\Leftrightarrow & 1400x-240x& = & 12-105 \\\Leftrightarrow & \color{red}{1160} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{1160} & & \\ & V = \left\{ \frac{-93}{1160} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{-54} & = & \color{red}{315x} +56 \\\Leftrightarrow & -567x \color{red}{-54} \color{blue}{+54} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+54} \\\Leftrightarrow & -567x-315x& = & 56+54 \\\Leftrightarrow & \color{red}{-882} x& = & 110 \\\Leftrightarrow & x = \frac{110}{-882} & & \\\Leftrightarrow & x = \frac{-55}{441} & & \\ & V = \left\{ \frac{-55}{441} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{4})& = & -9x+\frac{5}{7} \\\Leftrightarrow & 14x+\frac{35}{4}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{392}{ \color{blue}{28} }x+ \frac{245}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{20}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 392x \color{red}{+245} & = & \color{red}{-252x} +20 \\\Leftrightarrow & 392x \color{red}{+245} \color{blue}{-245} \color{blue}{+252x} & = & \color{red}{-252x} +20 \color{blue}{+252x} \color{blue}{-245} \\\Leftrightarrow & 392x+252x& = & 20-245 \\\Leftrightarrow & \color{red}{644} x& = & -225 \\\Leftrightarrow & x = \frac{-225}{644} & & \\ & V = \left\{ \frac{-225}{644} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 4x+\frac{4}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+44} & = & \color{red}{385x} +35 \\\Leftrightarrow & 308x \color{red}{+44} \color{blue}{-44} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{-44} \\\Leftrightarrow & 308x-385x& = & 35-44 \\\Leftrightarrow & \color{red}{-77} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-77} & & \\\Leftrightarrow & x = \frac{9}{77} & & \\ & V = \left\{ \frac{9}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{+12} & = & \color{red}{50x} +7 \\\Leftrightarrow & 80x \color{red}{+12} \color{blue}{-12} \color{blue}{-50x} & = & \color{red}{50x} +7 \color{blue}{-50x} \color{blue}{-12} \\\Leftrightarrow & 80x-50x& = & 7-12 \\\Leftrightarrow & \color{red}{30} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{30} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+180} \\\Leftrightarrow & -1260x+441x& = & 14+180 \\\Leftrightarrow & \color{red}{-819} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-819} & & \\\Leftrightarrow & x = \frac{-194}{819} & & \\ & V = \left\{ \frac{-194}{819} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{7})& = & -9x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-80} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -700x \color{red}{-80} \color{blue}{+80} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{+80} \\\Leftrightarrow & -700x+315x& = & 56+80 \\\Leftrightarrow & \color{red}{-385} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-385} & & \\\Leftrightarrow & x = \frac{-136}{385} & & \\ & V = \left\{ \frac{-136}{385} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{5})& = & 8x+\frac{10}{11} \\\Leftrightarrow & -21x+\frac{14}{5}& = & 8x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1155}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{440x} +50 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{-440x} & = & \color{red}{440x} +50 \color{blue}{-440x} \color{blue}{-154} \\\Leftrightarrow & -1155x-440x& = & 50-154 \\\Leftrightarrow & \color{red}{-1595} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1595} & & \\\Leftrightarrow & x = \frac{104}{1595} & & \\ & V = \left\{ \frac{104}{1595} \right\} & \\\end{align}\)
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