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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -30x+\frac{12}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-840}{ \color{blue}{28} }x+ \frac{48}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -840x \color{red}{+48} & = & \color{red}{196x} +21 \\\Leftrightarrow & -840x \color{red}{+48} \color{blue}{-48} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-48} \\\Leftrightarrow & -840x-196x& = & 21-48 \\\Leftrightarrow & \color{red}{-1036} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-1036} & & \\\Leftrightarrow & x = \frac{27}{1036} & & \\ & V = \left\{ \frac{27}{1036} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{9})& = & -9x+\frac{7}{10} \\\Leftrightarrow & -8x+\frac{4}{9}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-720}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} })& = & (\frac{-810}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -720x \color{red}{+40} & = & \color{red}{-810x} +63 \\\Leftrightarrow & -720x \color{red}{+40} \color{blue}{-40} \color{blue}{+810x} & = & \color{red}{-810x} +63 \color{blue}{+810x} \color{blue}{-40} \\\Leftrightarrow & -720x+810x& = & 63-40 \\\Leftrightarrow & \color{red}{90} x& = & 23 \\\Leftrightarrow & x = \frac{23}{90} & & \\ & V = \left\{ \frac{23}{90} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{+12} & = & \color{red}{45x} +2 \\\Leftrightarrow & -100x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +2 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & -100x-45x& = & 2-12 \\\Leftrightarrow & \color{red}{-145} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-145} & & \\\Leftrightarrow & x = \frac{2}{29} & & \\ & V = \left\{ \frac{2}{29} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{3})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 15x-\frac{10}{3}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{40}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{84x} +9 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{+40} \\\Leftrightarrow & 180x-84x& = & 9+40 \\\Leftrightarrow & \color{red}{96} x& = & 49 \\\Leftrightarrow & x = \frac{49}{96} & & \\ & V = \left\{ \frac{49}{96} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{5}{6})& = & -8x+\frac{5}{6} \\\Leftrightarrow & 21x-\frac{35}{6}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-35} & = & \color{red}{-48x} +5 \\\Leftrightarrow & 126x \color{red}{-35} \color{blue}{+35} \color{blue}{+48x} & = & \color{red}{-48x} +5 \color{blue}{+48x} \color{blue}{+35} \\\Leftrightarrow & 126x+48x& = & 5+35 \\\Leftrightarrow & \color{red}{174} x& = & 40 \\\Leftrightarrow & x = \frac{40}{174} & & \\\Leftrightarrow & x = \frac{20}{87} & & \\ & V = \left\{ \frac{20}{87} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{15}{8}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{-45} & = & \color{red}{120x} +32 \\\Leftrightarrow & -288x \color{red}{-45} \color{blue}{+45} \color{blue}{-120x} & = & \color{red}{120x} +32 \color{blue}{-120x} \color{blue}{+45} \\\Leftrightarrow & -288x-120x& = & 32+45 \\\Leftrightarrow & \color{red}{-408} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-408} & & \\\Leftrightarrow & x = \frac{-77}{408} & & \\ & V = \left\{ \frac{-77}{408} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{11})& = & -8x+\frac{7}{8} \\\Leftrightarrow & -28x-\frac{35}{11}& = & -8x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x- \frac{280}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{-280} & = & \color{red}{-704x} +77 \\\Leftrightarrow & -2464x \color{red}{-280} \color{blue}{+280} \color{blue}{+704x} & = & \color{red}{-704x} +77 \color{blue}{+704x} \color{blue}{+280} \\\Leftrightarrow & -2464x+704x& = & 77+280 \\\Leftrightarrow & \color{red}{-1760} x& = & 357 \\\Leftrightarrow & x = \frac{357}{-1760} & & \\\Leftrightarrow & x = \frac{-357}{1760} & & \\ & V = \left\{ \frac{-357}{1760} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{+32} & = & \color{red}{252x} +63 \\\Leftrightarrow & 216x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & 216x-252x& = & 63-32 \\\Leftrightarrow & \color{red}{-36} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-36} & & \\\Leftrightarrow & x = \frac{-31}{36} & & \\ & V = \left\{ \frac{-31}{36} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{+40} & = & \color{red}{42x} +63 \\\Leftrightarrow & 280x \color{red}{+40} \color{blue}{-40} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{-40} \\\Leftrightarrow & 280x-42x& = & 63-40 \\\Leftrightarrow & \color{red}{238} x& = & 23 \\\Leftrightarrow & x = \frac{23}{238} & & \\ & V = \left\{ \frac{23}{238} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-18} & = & \color{red}{105x} +40 \\\Leftrightarrow & -90x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & -90x-105x& = & 40+18 \\\Leftrightarrow & \color{red}{-195} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-195} & & \\\Leftrightarrow & x = \frac{-58}{195} & & \\ & V = \left\{ \frac{-58}{195} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{18}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{54}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+54} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -450x \color{red}{+54} \color{blue}{-54} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-54} \\\Leftrightarrow & -450x+105x& = & 40-54 \\\Leftrightarrow & \color{red}{-345} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-345} & & \\\Leftrightarrow & x = \frac{14}{345} & & \\ & V = \left\{ \frac{14}{345} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{6}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{-50x} +35 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{+12} \\\Leftrightarrow & -120x+50x& = & 35+12 \\\Leftrightarrow & \color{red}{-70} x& = & 47 \\\Leftrightarrow & x = \frac{47}{-70} & & \\\Leftrightarrow & x = \frac{-47}{70} & & \\ & V = \left\{ \frac{-47}{70} \right\} & \\\end{align}\)
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