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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{2})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{9}{2}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+45} & = & \color{red}{-50x} +12 \\\Leftrightarrow & 60x \color{red}{+45} \color{blue}{-45} \color{blue}{+50x} & = & \color{red}{-50x} +12 \color{blue}{+50x} \color{blue}{-45} \\\Leftrightarrow & 60x+50x& = & 12-45 \\\Leftrightarrow & \color{red}{110} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{110} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{2})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{21}{2}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{350}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 350x \color{red}{-105} & = & \color{red}{-30x} +12 \\\Leftrightarrow & 350x \color{red}{-105} \color{blue}{+105} \color{blue}{+30x} & = & \color{red}{-30x} +12 \color{blue}{+30x} \color{blue}{+105} \\\Leftrightarrow & 350x+30x& = & 12+105 \\\Leftrightarrow & \color{red}{380} x& = & 117 \\\Leftrightarrow & x = \frac{117}{380} & & \\ & V = \left\{ \frac{117}{380} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{8}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-88} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 330x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & 330x+297x& = & 18+88 \\\Leftrightarrow & \color{red}{627} x& = & 106 \\\Leftrightarrow & x = \frac{106}{627} & & \\ & V = \left\{ \frac{106}{627} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{25x} +4 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & 60x-25x& = & 4-12 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & 6x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{210x} +42 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{-210x} & = & \color{red}{210x} +42 \color{blue}{-210x} \color{blue}{+150} \\\Leftrightarrow & -630x-210x& = & 42+150 \\\Leftrightarrow & \color{red}{-840} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-840} & & \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{9})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 28x-\frac{14}{9}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x- \frac{28}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{-28} & = & \color{red}{54x} +27 \\\Leftrightarrow & 504x \color{red}{-28} \color{blue}{+28} \color{blue}{-54x} & = & \color{red}{54x} +27 \color{blue}{-54x} \color{blue}{+28} \\\Leftrightarrow & 504x-54x& = & 27+28 \\\Leftrightarrow & \color{red}{450} x& = & 55 \\\Leftrightarrow & x = \frac{55}{450} & & \\\Leftrightarrow & x = \frac{11}{90} & & \\ & V = \left\{ \frac{11}{90} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{3}{5})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 9x+\frac{9}{5}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{+9} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 45x \color{red}{+9} \color{blue}{-9} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{-9} \\\Leftrightarrow & 45x+35x& = & 4-9 \\\Leftrightarrow & \color{red}{80} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{80} & & \\\Leftrightarrow & x = \frac{-1}{16} & & \\ & V = \left\{ \frac{-1}{16} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{2})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -9x+\frac{9}{2}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-162}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -162x \color{red}{+81} & = & \color{red}{-90x} +4 \\\Leftrightarrow & -162x \color{red}{+81} \color{blue}{-81} \color{blue}{+90x} & = & \color{red}{-90x} +4 \color{blue}{+90x} \color{blue}{-81} \\\Leftrightarrow & -162x+90x& = & 4-81 \\\Leftrightarrow & \color{red}{-72} x& = & -77 \\\Leftrightarrow & x = \frac{-77}{-72} & & \\\Leftrightarrow & x = \frac{77}{72} & & \\ & V = \left\{ \frac{77}{72} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+6} & = & \color{red}{49x} +3 \\\Leftrightarrow & 28x \color{red}{+6} \color{blue}{-6} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-6} \\\Leftrightarrow & 28x-49x& = & 3-6 \\\Leftrightarrow & \color{red}{-21} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-21} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-792}{ \color{blue}{132} }x+ \frac{180}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -792x \color{red}{+180} & = & \color{red}{924x} +55 \\\Leftrightarrow & -792x \color{red}{+180} \color{blue}{-180} \color{blue}{-924x} & = & \color{red}{924x} +55 \color{blue}{-924x} \color{blue}{-180} \\\Leftrightarrow & -792x-924x& = & 55-180 \\\Leftrightarrow & \color{red}{-1716} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1716} & & \\\Leftrightarrow & x = \frac{125}{1716} & & \\ & V = \left\{ \frac{125}{1716} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{8})& = & 5x+\frac{5}{12} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{120x} +10 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{-63} \\\Leftrightarrow & 336x-120x& = & 10-63 \\\Leftrightarrow & \color{red}{216} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{216} & & \\ & V = \left\{ \frac{-53}{216} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+16} & = & \color{red}{30x} +9 \\\Leftrightarrow & -80x \color{red}{+16} \color{blue}{-16} \color{blue}{-30x} & = & \color{red}{30x} +9 \color{blue}{-30x} \color{blue}{-16} \\\Leftrightarrow & -80x-30x& = & 9-16 \\\Leftrightarrow & \color{red}{-110} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-110} & & \\\Leftrightarrow & x = \frac{7}{110} & & \\ & V = \left\{ \frac{7}{110} \right\} & \\\end{align}\)
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