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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{12}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{12}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+12} & = & \color{red}{-55x} +6 \\\Leftrightarrow & 66x \color{red}{+12} \color{blue}{-12} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-12} \\\Leftrightarrow & 66x+55x& = & 6-12 \\\Leftrightarrow & \color{red}{121} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{121} & & \\ & V = \left\{ \frac{-6}{121} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{3})& = & 3x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{4}{3}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+4} & = & \color{red}{9x} +2 \\\Leftrightarrow & -24x \color{red}{+4} \color{blue}{-4} \color{blue}{-9x} & = & \color{red}{9x} +2 \color{blue}{-9x} \color{blue}{-4} \\\Leftrightarrow & -24x-9x& = & 2-4 \\\Leftrightarrow & \color{red}{-33} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-33} & & \\\Leftrightarrow & x = \frac{2}{33} & & \\ & V = \left\{ \frac{2}{33} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-30} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 315x \color{red}{-30} \color{blue}{+30} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+30} \\\Leftrightarrow & 315x+147x& = & 70+30 \\\Leftrightarrow & \color{red}{462} x& = & 100 \\\Leftrightarrow & x = \frac{100}{462} & & \\\Leftrightarrow & x = \frac{50}{231} & & \\ & V = \left\{ \frac{50}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{4}{3})& = & -5x+\frac{9}{11} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+308} & = & \color{red}{-165x} +27 \\\Leftrightarrow & 462x \color{red}{+308} \color{blue}{-308} \color{blue}{+165x} & = & \color{red}{-165x} +27 \color{blue}{+165x} \color{blue}{-308} \\\Leftrightarrow & 462x+165x& = & 27-308 \\\Leftrightarrow & \color{red}{627} x& = & -281 \\\Leftrightarrow & x = \frac{-281}{627} & & \\ & V = \left\{ \frac{-281}{627} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{6}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+18} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -60x \color{red}{+18} \color{blue}{-18} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{-18} \\\Leftrightarrow & -60x+135x& = & 10-18 \\\Leftrightarrow & \color{red}{75} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{75} & & \\ & V = \left\{ \frac{-8}{75} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{3})& = & -4x+\frac{8}{9} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -4x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{105}{ \color{blue}{9} })& = & (\frac{-36}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-105} & = & \color{red}{-36x} +8 \\\Leftrightarrow & -315x \color{red}{-105} \color{blue}{+105} \color{blue}{+36x} & = & \color{red}{-36x} +8 \color{blue}{+36x} \color{blue}{+105} \\\Leftrightarrow & -315x+36x& = & 8+105 \\\Leftrightarrow & \color{red}{-279} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-279} & & \\\Leftrightarrow & x = \frac{-113}{279} & & \\ & V = \left\{ \frac{-113}{279} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-216} & = & \color{red}{-315x} +10 \\\Leftrightarrow & 540x \color{red}{-216} \color{blue}{+216} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{+216} \\\Leftrightarrow & 540x+315x& = & 10+216 \\\Leftrightarrow & \color{red}{855} x& = & 226 \\\Leftrightarrow & x = \frac{226}{855} & & \\ & V = \left\{ \frac{226}{855} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 24x+\frac{18}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{18}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-18} \\\Leftrightarrow & 168x+35x& = & 10-18 \\\Leftrightarrow & \color{red}{203} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{203} & & \\ & V = \left\{ \frac{-8}{203} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -4x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+45} & = & \color{red}{-48x} +16 \\\Leftrightarrow & -180x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & -180x+48x& = & 16-45 \\\Leftrightarrow & \color{red}{-132} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-132} & & \\\Leftrightarrow & x = \frac{29}{132} & & \\ & V = \left\{ \frac{29}{132} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{3})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-220} & = & \color{red}{297x} +15 \\\Leftrightarrow & -660x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +15 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & -660x-297x& = & 15+220 \\\Leftrightarrow & \color{red}{-957} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-957} & & \\\Leftrightarrow & x = \frac{-235}{957} & & \\ & V = \left\{ \frac{-235}{957} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-40} & = & \color{red}{126x} +81 \\\Leftrightarrow & -360x \color{red}{-40} \color{blue}{+40} \color{blue}{-126x} & = & \color{red}{126x} +81 \color{blue}{-126x} \color{blue}{+40} \\\Leftrightarrow & -360x-126x& = & 81+40 \\\Leftrightarrow & \color{red}{-486} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-486} & & \\\Leftrightarrow & x = \frac{-121}{486} & & \\ & V = \left\{ \frac{-121}{486} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{8})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{15}{8}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{-105} & = & \color{red}{-392x} +80 \\\Leftrightarrow & 336x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +80 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & 336x+392x& = & 80+105 \\\Leftrightarrow & \color{red}{728} x& = & 185 \\\Leftrightarrow & x = \frac{185}{728} & & \\ & V = \left\{ \frac{185}{728} \right\} & \\\end{align}\)
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