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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{9})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 20x-\frac{20}{9}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-80} & = & \color{red}{-252x} +81 \\\Leftrightarrow & 720x \color{red}{-80} \color{blue}{+80} \color{blue}{+252x} & = & \color{red}{-252x} +81 \color{blue}{+252x} \color{blue}{+80} \\\Leftrightarrow & 720x+252x& = & 81+80 \\\Leftrightarrow & \color{red}{972} x& = & 161 \\\Leftrightarrow & x = \frac{161}{972} & & \\ & V = \left\{ \frac{161}{972} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{11})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -6x-\frac{8}{11}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-396}{ \color{blue}{66} }x- \frac{48}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -396x \color{red}{-48} & = & \color{red}{462x} +55 \\\Leftrightarrow & -396x \color{red}{-48} \color{blue}{+48} \color{blue}{-462x} & = & \color{red}{462x} +55 \color{blue}{-462x} \color{blue}{+48} \\\Leftrightarrow & -396x-462x& = & 55+48 \\\Leftrightarrow & \color{red}{-858} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-858} & & \\\Leftrightarrow & x = \frac{-103}{858} & & \\ & V = \left\{ \frac{-103}{858} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{5})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{8}{5}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{135x} +50 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-135x} & = & \color{red}{135x} +50 \color{blue}{-135x} \color{blue}{+24} \\\Leftrightarrow & -120x-135x& = & 50+24 \\\Leftrightarrow & \color{red}{-255} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-255} & & \\\Leftrightarrow & x = \frac{-74}{255} & & \\ & V = \left\{ \frac{-74}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{-225x} +40 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{+54} \\\Leftrightarrow & 270x+225x& = & 40+54 \\\Leftrightarrow & \color{red}{495} x& = & 94 \\\Leftrightarrow & x = \frac{94}{495} & & \\ & V = \left\{ \frac{94}{495} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-18} \\\Leftrightarrow & -126x+147x& = & 70-18 \\\Leftrightarrow & \color{red}{21} x& = & 52 \\\Leftrightarrow & x = \frac{52}{21} & & \\ & V = \left\{ \frac{52}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{-63} & = & \color{red}{-192x} +64 \\\Leftrightarrow & -504x \color{red}{-63} \color{blue}{+63} \color{blue}{+192x} & = & \color{red}{-192x} +64 \color{blue}{+192x} \color{blue}{+63} \\\Leftrightarrow & -504x+192x& = & 64+63 \\\Leftrightarrow & \color{red}{-312} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-312} & & \\\Leftrightarrow & x = \frac{-127}{312} & & \\ & V = \left\{ \frac{-127}{312} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -10x+\frac{8}{3}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{+64} & = & \color{red}{168x} +21 \\\Leftrightarrow & -240x \color{red}{+64} \color{blue}{-64} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{-64} \\\Leftrightarrow & -240x-168x& = & 21-64 \\\Leftrightarrow & \color{red}{-408} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-408} & & \\\Leftrightarrow & x = \frac{43}{408} & & \\ & V = \left\{ \frac{43}{408} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{360}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 360x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 360x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 360x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{285} x& = & 46 \\\Leftrightarrow & x = \frac{46}{285} & & \\ & V = \left\{ \frac{46}{285} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{4}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -90x+50x& = & 15+24 \\\Leftrightarrow & \color{red}{-40} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-40} & & \\\Leftrightarrow & x = \frac{-39}{40} & & \\ & V = \left\{ \frac{-39}{40} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{11})& = & 5x+\frac{7}{4} \\\Leftrightarrow & -12x+\frac{15}{11}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{60}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+60} & = & \color{red}{220x} +77 \\\Leftrightarrow & -528x \color{red}{+60} \color{blue}{-60} \color{blue}{-220x} & = & \color{red}{220x} +77 \color{blue}{-220x} \color{blue}{-60} \\\Leftrightarrow & -528x-220x& = & 77-60 \\\Leftrightarrow & \color{red}{-748} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-748} & & \\\Leftrightarrow & x = \frac{-1}{44} & & \\ & V = \left\{ \frac{-1}{44} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-720}{ \color{blue}{30} }x+ \frac{144}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -720x \color{red}{+144} & = & \color{red}{150x} +25 \\\Leftrightarrow & -720x \color{red}{+144} \color{blue}{-144} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{-144} \\\Leftrightarrow & -720x-150x& = & 25-144 \\\Leftrightarrow & \color{red}{-870} x& = & -119 \\\Leftrightarrow & x = \frac{-119}{-870} & & \\\Leftrightarrow & x = \frac{119}{870} & & \\ & V = \left\{ \frac{119}{870} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{30}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+120} & = & \color{red}{-220x} +33 \\\Leftrightarrow & -528x \color{red}{+120} \color{blue}{-120} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{-120} \\\Leftrightarrow & -528x+220x& = & 33-120 \\\Leftrightarrow & \color{red}{-308} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-308} & & \\\Leftrightarrow & x = \frac{87}{308} & & \\ & V = \left\{ \frac{87}{308} \right\} & \\\end{align}\)
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