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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{11})& = & -7x+\frac{3}{8} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{-616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{+80} & = & \color{red}{-616x} +33 \\\Leftrightarrow & -880x \color{red}{+80} \color{blue}{-80} \color{blue}{+616x} & = & \color{red}{-616x} +33 \color{blue}{+616x} \color{blue}{-80} \\\Leftrightarrow & -880x+616x& = & 33-80 \\\Leftrightarrow & \color{red}{-264} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-264} & & \\\Leftrightarrow & x = \frac{47}{264} & & \\ & V = \left\{ \frac{47}{264} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{8})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{15}{8}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1056}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1056x \color{red}{-165} & = & \color{red}{440x} +32 \\\Leftrightarrow & -1056x \color{red}{-165} \color{blue}{+165} \color{blue}{-440x} & = & \color{red}{440x} +32 \color{blue}{-440x} \color{blue}{+165} \\\Leftrightarrow & -1056x-440x& = & 32+165 \\\Leftrightarrow & \color{red}{-1496} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1496} & & \\\Leftrightarrow & x = \frac{-197}{1496} & & \\ & V = \left\{ \frac{-197}{1496} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+90} & = & \color{red}{275x} +22 \\\Leftrightarrow & 660x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & 660x-275x& = & 22-90 \\\Leftrightarrow & \color{red}{385} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{385} & & \\ & V = \left\{ \frac{-68}{385} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & -4x+\frac{6}{7} \\\Leftrightarrow & -18x-\frac{24}{5}& = & -4x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-168} & = & \color{red}{-140x} +30 \\\Leftrightarrow & -630x \color{red}{-168} \color{blue}{+168} \color{blue}{+140x} & = & \color{red}{-140x} +30 \color{blue}{+140x} \color{blue}{+168} \\\Leftrightarrow & -630x+140x& = & 30+168 \\\Leftrightarrow & \color{red}{-490} x& = & 198 \\\Leftrightarrow & x = \frac{198}{-490} & & \\\Leftrightarrow & x = \frac{-99}{245} & & \\ & V = \left\{ \frac{-99}{245} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 14x-\frac{35}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{245}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-245} & = & \color{red}{-315x} +18 \\\Leftrightarrow & 882x \color{red}{-245} \color{blue}{+245} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+245} \\\Leftrightarrow & 882x+315x& = & 18+245 \\\Leftrightarrow & \color{red}{1197} x& = & 263 \\\Leftrightarrow & x = \frac{263}{1197} & & \\ & V = \left\{ \frac{263}{1197} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 120x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{50} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{50} & & \\ & V = \left\{ \frac{-9}{50} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{7})& = & -7x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{10}{7}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-700}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -700x \color{red}{-40} & = & \color{red}{-196x} +63 \\\Leftrightarrow & -700x \color{red}{-40} \color{blue}{+40} \color{blue}{+196x} & = & \color{red}{-196x} +63 \color{blue}{+196x} \color{blue}{+40} \\\Leftrightarrow & -700x+196x& = & 63+40 \\\Leftrightarrow & \color{red}{-504} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-504} & & \\\Leftrightarrow & x = \frac{-103}{504} & & \\ & V = \left\{ \frac{-103}{504} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-108} & = & \color{red}{-315x} +50 \\\Leftrightarrow & -270x \color{red}{-108} \color{blue}{+108} \color{blue}{+315x} & = & \color{red}{-315x} +50 \color{blue}{+315x} \color{blue}{+108} \\\Leftrightarrow & -270x+315x& = & 50+108 \\\Leftrightarrow & \color{red}{45} x& = & 158 \\\Leftrightarrow & x = \frac{158}{45} & & \\ & V = \left\{ \frac{158}{45} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-2)& = & -9x+\frac{7}{9} \\\Leftrightarrow & -35x+14& = & -9x+\frac{7}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x+ \frac{126}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{+126} & = & \color{red}{-81x} +7 \\\Leftrightarrow & -315x \color{red}{+126} \color{blue}{-126} \color{blue}{+81x} & = & \color{red}{-81x} +7 \color{blue}{+81x} \color{blue}{-126} \\\Leftrightarrow & -315x+81x& = & 7-126 \\\Leftrightarrow & \color{red}{-234} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-234} & & \\\Leftrightarrow & x = \frac{119}{234} & & \\ & V = \left\{ \frac{119}{234} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{5})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -14x-\frac{14}{5}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{-154} & = & \color{red}{-165x} +20 \\\Leftrightarrow & -770x \color{red}{-154} \color{blue}{+154} \color{blue}{+165x} & = & \color{red}{-165x} +20 \color{blue}{+165x} \color{blue}{+154} \\\Leftrightarrow & -770x+165x& = & 20+154 \\\Leftrightarrow & \color{red}{-605} x& = & 174 \\\Leftrightarrow & x = \frac{174}{-605} & & \\\Leftrightarrow & x = \frac{-174}{605} & & \\ & V = \left\{ \frac{-174}{605} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{+48} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 180x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & 180x+70x& = & 15-48 \\\Leftrightarrow & \color{red}{250} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{250} & & \\ & V = \left\{ \frac{-33}{250} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-9} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -30x \color{red}{-9} \color{blue}{+9} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+9} \\\Leftrightarrow & -30x+35x& = & 4+9 \\\Leftrightarrow & \color{red}{5} x& = & 13 \\\Leftrightarrow & x = \frac{13}{5} & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
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