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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 4x-\frac{10}{11}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-70} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 308x \color{red}{-70} \color{blue}{+70} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+70} \\\Leftrightarrow & 308x+231x& = & 88+70 \\\Leftrightarrow & \color{red}{539} x& = & 158 \\\Leftrightarrow & x = \frac{158}{539} & & \\ & V = \left\{ \frac{158}{539} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{50x} +15 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +15 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -120x-50x& = & 15+24 \\\Leftrightarrow & \color{red}{-170} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-170} & & \\\Leftrightarrow & x = \frac{-39}{170} & & \\ & V = \left\{ \frac{-39}{170} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{2}{7})& = & 8x+\frac{9}{8} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 8x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-840}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -840x \color{red}{-80} & = & \color{red}{448x} +63 \\\Leftrightarrow & -840x \color{red}{-80} \color{blue}{+80} \color{blue}{-448x} & = & \color{red}{448x} +63 \color{blue}{-448x} \color{blue}{+80} \\\Leftrightarrow & -840x-448x& = & 63+80 \\\Leftrightarrow & \color{red}{-1288} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1288} & & \\\Leftrightarrow & x = \frac{-143}{1288} & & \\ & V = \left\{ \frac{-143}{1288} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+168} & = & \color{red}{-315x} +45 \\\Leftrightarrow & -630x \color{red}{+168} \color{blue}{-168} \color{blue}{+315x} & = & \color{red}{-315x} +45 \color{blue}{+315x} \color{blue}{-168} \\\Leftrightarrow & -630x+315x& = & 45-168 \\\Leftrightarrow & \color{red}{-315} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-315} & & \\\Leftrightarrow & x = \frac{41}{105} & & \\ & V = \left\{ \frac{41}{105} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{189x} +18 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & 168x-189x& = & 18+56 \\\Leftrightarrow & \color{red}{-21} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-21} & & \\\Leftrightarrow & x = \frac{-74}{21} & & \\ & V = \left\{ \frac{-74}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{2}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-56} & = & \color{red}{189x} +30 \\\Leftrightarrow & -168x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & -168x-189x& = & 30+56 \\\Leftrightarrow & \color{red}{-357} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-357} & & \\\Leftrightarrow & x = \frac{-86}{357} & & \\ & V = \left\{ \frac{-86}{357} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{5})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 8x-\frac{16}{5}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{80}{ \color{blue}{10} }x- \frac{32}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 80x \color{red}{-32} & = & \color{red}{-90x} +25 \\\Leftrightarrow & 80x \color{red}{-32} \color{blue}{+32} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{+32} \\\Leftrightarrow & 80x+90x& = & 25+32 \\\Leftrightarrow & \color{red}{170} x& = & 57 \\\Leftrightarrow & x = \frac{57}{170} & & \\ & V = \left\{ \frac{57}{170} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{-18} & = & \color{red}{42x} +28 \\\Leftrightarrow & 189x \color{red}{-18} \color{blue}{+18} \color{blue}{-42x} & = & \color{red}{42x} +28 \color{blue}{-42x} \color{blue}{+18} \\\Leftrightarrow & 189x-42x& = & 28+18 \\\Leftrightarrow & \color{red}{147} x& = & 46 \\\Leftrightarrow & x = \frac{46}{147} & & \\ & V = \left\{ \frac{46}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 24x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & 840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & 840x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{1015} x& = & 99 \\\Leftrightarrow & x = \frac{99}{1015} & & \\ & V = \left\{ \frac{99}{1015} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 10x+\frac{10}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+50} & = & \color{red}{105x} +6 \\\Leftrightarrow & 150x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 150x-105x& = & 6-50 \\\Leftrightarrow & \color{red}{45} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{45} & & \\ & V = \left\{ \frac{-44}{45} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-440}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -440x \color{red}{+100} & = & \color{red}{990x} +33 \\\Leftrightarrow & -440x \color{red}{+100} \color{blue}{-100} \color{blue}{-990x} & = & \color{red}{990x} +33 \color{blue}{-990x} \color{blue}{-100} \\\Leftrightarrow & -440x-990x& = & 33-100 \\\Leftrightarrow & \color{red}{-1430} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{-1430} & & \\\Leftrightarrow & x = \frac{67}{1430} & & \\ & V = \left\{ \frac{67}{1430} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{105x} +30 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{-56} \\\Leftrightarrow & 252x-105x& = & 30-56 \\\Leftrightarrow & \color{red}{147} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{147} & & \\ & V = \left\{ \frac{-26}{147} \right\} & \\\end{align}\)
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