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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{-12} \\\Leftrightarrow & -60x-25x& = & 6-12 \\\Leftrightarrow & \color{red}{-85} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-85} & & \\\Leftrightarrow & x = \frac{6}{85} & & \\ & V = \left\{ \frac{6}{85} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{8})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -28x+\frac{35}{8}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2464}{ \color{blue}{88} }x+ \frac{385}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2464x \color{red}{+385} & = & \color{red}{264x} +32 \\\Leftrightarrow & -2464x \color{red}{+385} \color{blue}{-385} \color{blue}{-264x} & = & \color{red}{264x} +32 \color{blue}{-264x} \color{blue}{-385} \\\Leftrightarrow & -2464x-264x& = & 32-385 \\\Leftrightarrow & \color{red}{-2728} x& = & -353 \\\Leftrightarrow & x = \frac{-353}{-2728} & & \\\Leftrightarrow & x = \frac{353}{2728} & & \\ & V = \left\{ \frac{353}{2728} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 4x-\frac{10}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-70} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 308x \color{red}{-70} \color{blue}{+70} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+70} \\\Leftrightarrow & 308x+385x& = & 33+70 \\\Leftrightarrow & \color{red}{693} x& = & 103 \\\Leftrightarrow & x = \frac{103}{693} & & \\ & V = \left\{ \frac{103}{693} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -8x+\frac{10}{11} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x+ \frac{231}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{+231} & = & \color{red}{-176x} +20 \\\Leftrightarrow & 462x \color{red}{+231} \color{blue}{-231} \color{blue}{+176x} & = & \color{red}{-176x} +20 \color{blue}{+176x} \color{blue}{-231} \\\Leftrightarrow & 462x+176x& = & 20-231 \\\Leftrightarrow & \color{red}{638} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{638} & & \\ & V = \left\{ \frac{-211}{638} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{2})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{15}{2}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-45} & = & \color{red}{-42x} +8 \\\Leftrightarrow & 90x \color{red}{-45} \color{blue}{+45} \color{blue}{+42x} & = & \color{red}{-42x} +8 \color{blue}{+42x} \color{blue}{+45} \\\Leftrightarrow & 90x+42x& = & 8+45 \\\Leftrightarrow & \color{red}{132} x& = & 53 \\\Leftrightarrow & x = \frac{53}{132} & & \\ & V = \left\{ \frac{53}{132} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{11})& = & 9x+\frac{9}{4} \\\Leftrightarrow & -25x-\frac{25}{11}& = & 9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x- \frac{100}{ \color{blue}{44} })& = & (\frac{396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{-100} & = & \color{red}{396x} +99 \\\Leftrightarrow & -1100x \color{red}{-100} \color{blue}{+100} \color{blue}{-396x} & = & \color{red}{396x} +99 \color{blue}{-396x} \color{blue}{+100} \\\Leftrightarrow & -1100x-396x& = & 99+100 \\\Leftrightarrow & \color{red}{-1496} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1496} & & \\\Leftrightarrow & x = \frac{-199}{1496} & & \\ & V = \left\{ \frac{-199}{1496} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{480}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 480x \color{red}{-72} & = & \color{red}{-270x} +25 \\\Leftrightarrow & 480x \color{red}{-72} \color{blue}{+72} \color{blue}{+270x} & = & \color{red}{-270x} +25 \color{blue}{+270x} \color{blue}{+72} \\\Leftrightarrow & 480x+270x& = & 25+72 \\\Leftrightarrow & \color{red}{750} x& = & 97 \\\Leftrightarrow & x = \frac{97}{750} & & \\ & V = \left\{ \frac{97}{750} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{11})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 24x-\frac{12}{11}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-60} & = & \color{red}{-275x} +77 \\\Leftrightarrow & 1320x \color{red}{-60} \color{blue}{+60} \color{blue}{+275x} & = & \color{red}{-275x} +77 \color{blue}{+275x} \color{blue}{+60} \\\Leftrightarrow & 1320x+275x& = & 77+60 \\\Leftrightarrow & \color{red}{1595} x& = & 137 \\\Leftrightarrow & x = \frac{137}{1595} & & \\ & V = \left\{ \frac{137}{1595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{9})& = & 6x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{28}{9}& = & 6x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x- \frac{56}{ \color{blue}{18} })& = & (\frac{108}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{-56} & = & \color{red}{108x} +81 \\\Leftrightarrow & -630x \color{red}{-56} \color{blue}{+56} \color{blue}{-108x} & = & \color{red}{108x} +81 \color{blue}{-108x} \color{blue}{+56} \\\Leftrightarrow & -630x-108x& = & 81+56 \\\Leftrightarrow & \color{red}{-738} x& = & 137 \\\Leftrightarrow & x = \frac{137}{-738} & & \\\Leftrightarrow & x = \frac{-137}{738} & & \\ & V = \left\{ \frac{-137}{738} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 4x+\frac{4}{9}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{81}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+44} & = & \color{red}{-693x} +81 \\\Leftrightarrow & 396x \color{red}{+44} \color{blue}{-44} \color{blue}{+693x} & = & \color{red}{-693x} +81 \color{blue}{+693x} \color{blue}{-44} \\\Leftrightarrow & 396x+693x& = & 81-44 \\\Leftrightarrow & \color{red}{1089} x& = & 37 \\\Leftrightarrow & x = \frac{37}{1089} & & \\ & V = \left\{ \frac{37}{1089} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{10}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-10} & = & \color{red}{81x} +6 \\\Leftrightarrow & -72x \color{red}{-10} \color{blue}{+10} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{+10} \\\Leftrightarrow & -72x-81x& = & 6+10 \\\Leftrightarrow & \color{red}{-153} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-153} & & \\\Leftrightarrow & x = \frac{-16}{153} & & \\ & V = \left\{ \frac{-16}{153} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{11})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{385x} +22 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-30} \\\Leftrightarrow & -330x-385x& = & 22-30 \\\Leftrightarrow & \color{red}{-715} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-715} & & \\\Leftrightarrow & x = \frac{8}{715} & & \\ & V = \left\{ \frac{8}{715} \right\} & \\\end{align}\)
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