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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{2}{3})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 16x-\frac{8}{3}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{96}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 96x \color{red}{-16} & = & \color{red}{-54x} +21 \\\Leftrightarrow & 96x \color{red}{-16} \color{blue}{+16} \color{blue}{+54x} & = & \color{red}{-54x} +21 \color{blue}{+54x} \color{blue}{+16} \\\Leftrightarrow & 96x+54x& = & 21+16 \\\Leftrightarrow & \color{red}{150} x& = & 37 \\\Leftrightarrow & x = \frac{37}{150} & & \\ & V = \left\{ \frac{37}{150} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{11})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{16}{11}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{-495x} +66 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{+495x} & = & \color{red}{-495x} +66 \color{blue}{+495x} \color{blue}{-80} \\\Leftrightarrow & 880x+495x& = & 66-80 \\\Leftrightarrow & \color{red}{1375} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{1375} & & \\ & V = \left\{ \frac{-14}{1375} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{6})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 20x+\frac{25}{6}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+25} & = & \color{red}{-42x} +7 \\\Leftrightarrow & 120x \color{red}{+25} \color{blue}{-25} \color{blue}{+42x} & = & \color{red}{-42x} +7 \color{blue}{+42x} \color{blue}{-25} \\\Leftrightarrow & 120x+42x& = & 7-25 \\\Leftrightarrow & \color{red}{162} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{162} & & \\\Leftrightarrow & x = \frac{-1}{9} & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{2}{9})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{-8} & = & \color{red}{63x} +4 \\\Leftrightarrow & 180x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & 180x-63x& = & 4+8 \\\Leftrightarrow & \color{red}{117} x& = & 12 \\\Leftrightarrow & x = \frac{12}{117} & & \\\Leftrightarrow & x = \frac{4}{39} & & \\ & V = \left\{ \frac{4}{39} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+196} & = & \color{red}{-189x} +27 \\\Leftrightarrow & 588x \color{red}{+196} \color{blue}{-196} \color{blue}{+189x} & = & \color{red}{-189x} +27 \color{blue}{+189x} \color{blue}{-196} \\\Leftrightarrow & 588x+189x& = & 27-196 \\\Leftrightarrow & \color{red}{777} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{777} & & \\ & V = \left\{ \frac{-169}{777} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 6x-\frac{4}{3}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{+28} \\\Leftrightarrow & 126x+105x& = & 18+28 \\\Leftrightarrow & \color{red}{231} x& = & 46 \\\Leftrightarrow & x = \frac{46}{231} & & \\ & V = \left\{ \frac{46}{231} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{4})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -9x+\frac{15}{4}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{+15} & = & \color{red}{-28x} +18 \\\Leftrightarrow & -36x \color{red}{+15} \color{blue}{-15} \color{blue}{+28x} & = & \color{red}{-28x} +18 \color{blue}{+28x} \color{blue}{-15} \\\Leftrightarrow & -36x+28x& = & 18-15 \\\Leftrightarrow & \color{red}{-8} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-8} & & \\\Leftrightarrow & x = \frac{-3}{8} & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{6})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{25}{6}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{126}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-175} & = & \color{red}{126x} +48 \\\Leftrightarrow & -840x \color{red}{-175} \color{blue}{+175} \color{blue}{-126x} & = & \color{red}{126x} +48 \color{blue}{-126x} \color{blue}{+175} \\\Leftrightarrow & -840x-126x& = & 48+175 \\\Leftrightarrow & \color{red}{-966} x& = & 223 \\\Leftrightarrow & x = \frac{223}{-966} & & \\\Leftrightarrow & x = \frac{-223}{966} & & \\ & V = \left\{ \frac{-223}{966} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{7})& = & 5x+\frac{7}{9} \\\Leftrightarrow & -12x-\frac{20}{7}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-180} & = & \color{red}{315x} +49 \\\Leftrightarrow & -756x \color{red}{-180} \color{blue}{+180} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{+180} \\\Leftrightarrow & -756x-315x& = & 49+180 \\\Leftrightarrow & \color{red}{-1071} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1071} & & \\\Leftrightarrow & x = \frac{-229}{1071} & & \\ & V = \left\{ \frac{-229}{1071} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{9})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{25}{9}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1485}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1485x \color{red}{-275} & = & \color{red}{396x} +90 \\\Leftrightarrow & -1485x \color{red}{-275} \color{blue}{+275} \color{blue}{-396x} & = & \color{red}{396x} +90 \color{blue}{-396x} \color{blue}{+275} \\\Leftrightarrow & -1485x-396x& = & 90+275 \\\Leftrightarrow & \color{red}{-1881} x& = & 365 \\\Leftrightarrow & x = \frac{365}{-1881} & & \\\Leftrightarrow & x = \frac{-365}{1881} & & \\ & V = \left\{ \frac{-365}{1881} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+10} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{-10} \\\Leftrightarrow & -12x+27x& = & 4-10 \\\Leftrightarrow & \color{red}{15} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{15} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{9})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 6x-\frac{8}{9}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{-56} & = & \color{red}{-315x} +81 \\\Leftrightarrow & 378x \color{red}{-56} \color{blue}{+56} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{+56} \\\Leftrightarrow & 378x+315x& = & 81+56 \\\Leftrightarrow & \color{red}{693} x& = & 137 \\\Leftrightarrow & x = \frac{137}{693} & & \\ & V = \left\{ \frac{137}{693} \right\} & \\\end{align}\)
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