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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & 2x+\frac{7}{4} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 2x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{-40} & = & \color{red}{88x} +77 \\\Leftrightarrow & 1100x \color{red}{-40} \color{blue}{+40} \color{blue}{-88x} & = & \color{red}{88x} +77 \color{blue}{-88x} \color{blue}{+40} \\\Leftrightarrow & 1100x-88x& = & 77+40 \\\Leftrightarrow & \color{red}{1012} x& = & 117 \\\Leftrightarrow & x = \frac{117}{1012} & & \\ & V = \left\{ \frac{117}{1012} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -6x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -6x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-14} & = & \color{red}{-18x} +8 \\\Leftrightarrow & -105x \color{red}{-14} \color{blue}{+14} \color{blue}{+18x} & = & \color{red}{-18x} +8 \color{blue}{+18x} \color{blue}{+14} \\\Leftrightarrow & -105x+18x& = & 8+14 \\\Leftrightarrow & \color{red}{-87} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-87} & & \\\Leftrightarrow & x = \frac{-22}{87} & & \\ & V = \left\{ \frac{-22}{87} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{9}{11} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{9}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{72}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-231} & = & \color{red}{704x} +72 \\\Leftrightarrow & -1848x \color{red}{-231} \color{blue}{+231} \color{blue}{-704x} & = & \color{red}{704x} +72 \color{blue}{-704x} \color{blue}{+231} \\\Leftrightarrow & -1848x-704x& = & 72+231 \\\Leftrightarrow & \color{red}{-2552} x& = & 303 \\\Leftrightarrow & x = \frac{303}{-2552} & & \\\Leftrightarrow & x = \frac{-303}{2552} & & \\ & V = \left\{ \frac{-303}{2552} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-84} & = & \color{red}{105x} +45 \\\Leftrightarrow & -700x \color{red}{-84} \color{blue}{+84} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{+84} \\\Leftrightarrow & -700x-105x& = & 45+84 \\\Leftrightarrow & \color{red}{-805} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-805} & & \\\Leftrightarrow & x = \frac{-129}{805} & & \\ & V = \left\{ \frac{-129}{805} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 8x+\frac{5}{4} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 8x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{224}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+24} & = & \color{red}{224x} +35 \\\Leftrightarrow & 420x \color{red}{+24} \color{blue}{-24} \color{blue}{-224x} & = & \color{red}{224x} +35 \color{blue}{-224x} \color{blue}{-24} \\\Leftrightarrow & 420x-224x& = & 35-24 \\\Leftrightarrow & \color{red}{196} x& = & 11 \\\Leftrightarrow & x = \frac{11}{196} & & \\ & V = \left\{ \frac{11}{196} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{6})& = & -3x+\frac{2}{9} \\\Leftrightarrow & -28x+\frac{35}{6}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-504}{ \color{blue}{18} }x+ \frac{105}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -504x \color{red}{+105} & = & \color{red}{-54x} +4 \\\Leftrightarrow & -504x \color{red}{+105} \color{blue}{-105} \color{blue}{+54x} & = & \color{red}{-54x} +4 \color{blue}{+54x} \color{blue}{-105} \\\Leftrightarrow & -504x+54x& = & 4-105 \\\Leftrightarrow & \color{red}{-450} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{-450} & & \\\Leftrightarrow & x = \frac{101}{450} & & \\ & V = \left\{ \frac{101}{450} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{1}{3})& = & -5x+\frac{3}{4} \\\Leftrightarrow & 28x-\frac{7}{3}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{336}{ \color{blue}{12} }x- \frac{28}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 336x \color{red}{-28} & = & \color{red}{-60x} +9 \\\Leftrightarrow & 336x \color{red}{-28} \color{blue}{+28} \color{blue}{+60x} & = & \color{red}{-60x} +9 \color{blue}{+60x} \color{blue}{+28} \\\Leftrightarrow & 336x+60x& = & 9+28 \\\Leftrightarrow & \color{red}{396} x& = & 37 \\\Leftrightarrow & x = \frac{37}{396} & & \\ & V = \left\{ \frac{37}{396} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & 8x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{20}{3}& = & 8x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{+80} & = & \color{red}{96x} +7 \\\Leftrightarrow & -180x \color{red}{+80} \color{blue}{-80} \color{blue}{-96x} & = & \color{red}{96x} +7 \color{blue}{-96x} \color{blue}{-80} \\\Leftrightarrow & -180x-96x& = & 7-80 \\\Leftrightarrow & \color{red}{-276} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-276} & & \\\Leftrightarrow & x = \frac{73}{276} & & \\ & V = \left\{ \frac{73}{276} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 6x+\frac{10}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+90} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 378x \color{red}{+90} \color{blue}{-90} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-90} \\\Leftrightarrow & 378x+315x& = & 14-90 \\\Leftrightarrow & \color{red}{693} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{693} & & \\ & V = \left\{ \frac{-76}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-56} & = & \color{red}{189x} +30 \\\Leftrightarrow & -168x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & -168x-189x& = & 30+56 \\\Leftrightarrow & \color{red}{-357} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-357} & & \\\Leftrightarrow & x = \frac{-86}{357} & & \\ & V = \left\{ \frac{-86}{357} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{5})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+12} & = & \color{red}{45x} +6 \\\Leftrightarrow & -40x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & -40x-45x& = & 6-12 \\\Leftrightarrow & \color{red}{-85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-85} & & \\\Leftrightarrow & x = \frac{6}{85} & & \\ & V = \left\{ \frac{6}{85} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 9x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{90x} +45 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{-90x} & = & \color{red}{90x} +45 \color{blue}{-90x} \color{blue}{-24} \\\Leftrightarrow & -80x-90x& = & 45-24 \\\Leftrightarrow & \color{red}{-170} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-170} & & \\\Leftrightarrow & x = \frac{-21}{170} & & \\ & V = \left\{ \frac{-21}{170} \right\} & \\\end{align}\)
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