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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{-20} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 140x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & 140x+98x& = & 21+20 \\\Leftrightarrow & \color{red}{238} x& = & 41 \\\Leftrightarrow & x = \frac{41}{238} & & \\ & V = \left\{ \frac{41}{238} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{+60} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -840x \color{red}{+60} \color{blue}{-60} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{-60} \\\Leftrightarrow & -840x+350x& = & 63-60 \\\Leftrightarrow & \color{red}{-490} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-490} & & \\\Leftrightarrow & x = \frac{-3}{490} & & \\ & V = \left\{ \frac{-3}{490} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-660}{ \color{blue}{66} }x- \frac{90}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -660x \color{red}{-90} & = & \color{red}{462x} +77 \\\Leftrightarrow & -660x \color{red}{-90} \color{blue}{+90} \color{blue}{-462x} & = & \color{red}{462x} +77 \color{blue}{-462x} \color{blue}{+90} \\\Leftrightarrow & -660x-462x& = & 77+90 \\\Leftrightarrow & \color{red}{-1122} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-1122} & & \\\Leftrightarrow & x = \frac{-167}{1122} & & \\ & V = \left\{ \frac{-167}{1122} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{3})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{54x} +9 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-54x} & = & \color{red}{54x} +9 \color{blue}{-54x} \color{blue}{-16} \\\Leftrightarrow & -48x-54x& = & 9-16 \\\Leftrightarrow & \color{red}{-102} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-102} & & \\\Leftrightarrow & x = \frac{7}{102} & & \\ & V = \left\{ \frac{7}{102} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{+30} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -168x \color{red}{+30} \color{blue}{-30} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-30} \\\Leftrightarrow & -168x+35x& = & 10-30 \\\Leftrightarrow & \color{red}{-133} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-133} & & \\\Leftrightarrow & x = \frac{20}{133} & & \\ & V = \left\{ \frac{20}{133} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{-297x} +18 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+88} \\\Leftrightarrow & 264x+297x& = & 18+88 \\\Leftrightarrow & \color{red}{561} x& = & 106 \\\Leftrightarrow & x = \frac{106}{561} & & \\ & V = \left\{ \frac{106}{561} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+135} & = & \color{red}{-252x} +40 \\\Leftrightarrow & -216x \color{red}{+135} \color{blue}{-135} \color{blue}{+252x} & = & \color{red}{-252x} +40 \color{blue}{+252x} \color{blue}{-135} \\\Leftrightarrow & -216x+252x& = & 40-135 \\\Leftrightarrow & \color{red}{36} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{36} & & \\ & V = \left\{ \frac{-95}{36} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1512}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1512x \color{red}{+270} & = & \color{red}{315x} +14 \\\Leftrightarrow & -1512x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & -1512x-315x& = & 14-270 \\\Leftrightarrow & \color{red}{-1827} x& = & -256 \\\Leftrightarrow & x = \frac{-256}{-1827} & & \\\Leftrightarrow & x = \frac{256}{1827} & & \\ & V = \left\{ \frac{256}{1827} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{11})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -24x-\frac{12}{11}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{-108} & = & \color{red}{-495x} +77 \\\Leftrightarrow & -2376x \color{red}{-108} \color{blue}{+108} \color{blue}{+495x} & = & \color{red}{-495x} +77 \color{blue}{+495x} \color{blue}{+108} \\\Leftrightarrow & -2376x+495x& = & 77+108 \\\Leftrightarrow & \color{red}{-1881} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-1881} & & \\\Leftrightarrow & x = \frac{-185}{1881} & & \\ & V = \left\{ \frac{-185}{1881} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{3})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{10}{3}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-70} & = & \color{red}{-189x} +6 \\\Leftrightarrow & -168x \color{red}{-70} \color{blue}{+70} \color{blue}{+189x} & = & \color{red}{-189x} +6 \color{blue}{+189x} \color{blue}{+70} \\\Leftrightarrow & -168x+189x& = & 6+70 \\\Leftrightarrow & \color{red}{21} x& = & 76 \\\Leftrightarrow & x = \frac{76}{21} & & \\ & V = \left\{ \frac{76}{21} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{24}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+24} \\\Leftrightarrow & -120x+35x& = & 6+24 \\\Leftrightarrow & \color{red}{-85} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-85} & & \\\Leftrightarrow & x = \frac{-6}{17} & & \\ & V = \left\{ \frac{-6}{17} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+12} & = & \color{red}{42x} +49 \\\Leftrightarrow & 140x \color{red}{+12} \color{blue}{-12} \color{blue}{-42x} & = & \color{red}{42x} +49 \color{blue}{-42x} \color{blue}{-12} \\\Leftrightarrow & 140x-42x& = & 49-12 \\\Leftrightarrow & \color{red}{98} x& = & 37 \\\Leftrightarrow & x = \frac{37}{98} & & \\ & V = \left\{ \frac{37}{98} \right\} & \\\end{align}\)
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