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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -3x+\frac{5}{7} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -3x+\frac{5}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{20}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{-105} & = & \color{red}{-84x} +20 \\\Leftrightarrow & 700x \color{red}{-105} \color{blue}{+105} \color{blue}{+84x} & = & \color{red}{-84x} +20 \color{blue}{+84x} \color{blue}{+105} \\\Leftrightarrow & 700x+84x& = & 20+105 \\\Leftrightarrow & \color{red}{784} x& = & 125 \\\Leftrightarrow & x = \frac{125}{784} & & \\ & V = \left\{ \frac{125}{784} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & 9x+\frac{3}{8} \\\Leftrightarrow & 4x+\frac{10}{7}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{224}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 224x \color{red}{+80} & = & \color{red}{504x} +21 \\\Leftrightarrow & 224x \color{red}{+80} \color{blue}{-80} \color{blue}{-504x} & = & \color{red}{504x} +21 \color{blue}{-504x} \color{blue}{-80} \\\Leftrightarrow & 224x-504x& = & 21-80 \\\Leftrightarrow & \color{red}{-280} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-280} & & \\\Leftrightarrow & x = \frac{59}{280} & & \\ & V = \left\{ \frac{59}{280} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{11})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{12}{11}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+36} & = & \color{red}{-99x} +110 \\\Leftrightarrow & 264x \color{red}{+36} \color{blue}{-36} \color{blue}{+99x} & = & \color{red}{-99x} +110 \color{blue}{+99x} \color{blue}{-36} \\\Leftrightarrow & 264x+99x& = & 110-36 \\\Leftrightarrow & \color{red}{363} x& = & 74 \\\Leftrightarrow & x = \frac{74}{363} & & \\ & V = \left\{ \frac{74}{363} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{12})& = & -9x+\frac{10}{9} \\\Leftrightarrow & -28x+\frac{35}{12}& = & -9x+\frac{10}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-1008}{ \color{blue}{36} }x+ \frac{105}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -1008x \color{red}{+105} & = & \color{red}{-324x} +40 \\\Leftrightarrow & -1008x \color{red}{+105} \color{blue}{-105} \color{blue}{+324x} & = & \color{red}{-324x} +40 \color{blue}{+324x} \color{blue}{-105} \\\Leftrightarrow & -1008x+324x& = & 40-105 \\\Leftrightarrow & \color{red}{-684} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-684} & & \\\Leftrightarrow & x = \frac{65}{684} & & \\ & V = \left\{ \frac{65}{684} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 4x+\frac{8}{7}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+72} & = & \color{red}{-315x} +49 \\\Leftrightarrow & 252x \color{red}{+72} \color{blue}{-72} \color{blue}{+315x} & = & \color{red}{-315x} +49 \color{blue}{+315x} \color{blue}{-72} \\\Leftrightarrow & 252x+315x& = & 49-72 \\\Leftrightarrow & \color{red}{567} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{567} & & \\ & V = \left\{ \frac{-23}{567} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -14x-\frac{14}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{112}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-112} & = & \color{red}{-216x} +63 \\\Leftrightarrow & -1008x \color{red}{-112} \color{blue}{+112} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{+112} \\\Leftrightarrow & -1008x+216x& = & 63+112 \\\Leftrightarrow & \color{red}{-792} x& = & 175 \\\Leftrightarrow & x = \frac{175}{-792} & & \\\Leftrightarrow & x = \frac{-175}{792} & & \\ & V = \left\{ \frac{-175}{792} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{-20} & = & \color{red}{-9x} +10 \\\Leftrightarrow & 48x \color{red}{-20} \color{blue}{+20} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+20} \\\Leftrightarrow & 48x+9x& = & 10+20 \\\Leftrightarrow & \color{red}{57} x& = & 30 \\\Leftrightarrow & x = \frac{30}{57} & & \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{3})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{16}{3}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-112} & = & \color{red}{105x} +12 \\\Leftrightarrow & -252x \color{red}{-112} \color{blue}{+112} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{+112} \\\Leftrightarrow & -252x-105x& = & 12+112 \\\Leftrightarrow & \color{red}{-357} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-357} & & \\\Leftrightarrow & x = \frac{-124}{357} & & \\ & V = \left\{ \frac{-124}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{3})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{8}{3}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{+24} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -54x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & -54x+63x& = & 2-24 \\\Leftrightarrow & \color{red}{9} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{9} & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{3}{2})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{9}{2}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-24}{ \color{blue}{2} }x- \frac{9}{ \color{blue}{2} })& = & (\frac{10}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -24x \color{red}{-9} & = & \color{red}{10x} +9 \\\Leftrightarrow & -24x \color{red}{-9} \color{blue}{+9} \color{blue}{-10x} & = & \color{red}{10x} +9 \color{blue}{-10x} \color{blue}{+9} \\\Leftrightarrow & -24x-10x& = & 9+9 \\\Leftrightarrow & \color{red}{-34} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-34} & & \\\Leftrightarrow & x = \frac{-9}{17} & & \\ & V = \left\{ \frac{-9}{17} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{20}{9}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{81x} +30 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{-81x} & = & \color{red}{81x} +30 \color{blue}{-81x} \color{blue}{-20} \\\Leftrightarrow & -180x-81x& = & 30-20 \\\Leftrightarrow & \color{red}{-261} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-261} & & \\\Leftrightarrow & x = \frac{-10}{261} & & \\ & V = \left\{ \frac{-10}{261} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 15x-\frac{10}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{-20} & = & \color{red}{98x} +21 \\\Leftrightarrow & 210x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & 210x-98x& = & 21+20 \\\Leftrightarrow & \color{red}{112} x& = & 41 \\\Leftrightarrow & x = \frac{41}{112} & & \\ & V = \left\{ \frac{41}{112} \right\} & \\\end{align}\)
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