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Alles samen. Gebruik stappenplan en ZRM!

  1. \(6(-5x-\frac{5}{3})=29x+\frac{6}{11}\)
  2. \(-(-4x-\frac{3}{11})=9x+\frac{10}{13}\)
  3. \(-2(2x-\frac{4}{9})=-3x+\frac{2}{3}\)
  4. \(7(-2x+\frac{5}{14})=9x+\frac{6}{13}\)
  5. \(-5(-5x-\frac{2}{9})=7x+\frac{10}{9}\)
  6. \(3(-x+\frac{5}{7})=-5x+\frac{9}{8}\)
  7. \(7(-2x+\frac{4}{11})=3x+\frac{2}{9}\)
  8. \(-3(2x+\frac{4}{9})=7x+\frac{6}{7}\)
  9. \(5(-5x+\frac{4}{7})=-4x+\frac{4}{7}\)
  10. \(-3(-x-\frac{4}{5})=-8x+\frac{3}{7}\)
  11. \((2x-\frac{2}{13})=3x+\frac{7}{12}\)
  12. \(-5(3x+\frac{4}{9})=7x+\frac{3}{13}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{3})& = & 29x+\frac{6}{11} \\\Leftrightarrow & -30x-10& = & 29x+\frac{6}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(-30x-10)& = & (29x+\frac{6}{11}). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-110} & = & \color{red}{319x} +6 \\\Leftrightarrow & -330x \color{red}{-110} \color{blue}{+110} \color{blue}{-319x} & = & \color{red}{319x} +6 \color{blue}{-319x} \color{blue}{+110} \\\Leftrightarrow & -330x-319x& = & 6+110 \\\Leftrightarrow & \color{red}{-649} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-649} & & \\\Leftrightarrow & x = \frac{-116}{649} & & \\ & V = \left\{ \frac{-116}{649} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-} (-4x-\frac{3}{11})& = & 9x+\frac{10}{13} \\\Leftrightarrow & 4x+\frac{3}{11}& = & 9x+\frac{10}{13} \\ & & & \text{kgv van noemers 11 en 13 is 143} \\\Leftrightarrow & \color{blue}{143} .(4x+\frac{3}{11})& = & (9x+\frac{10}{13}). \color{blue}{143} \\\Leftrightarrow & 572x \color{red}{+39} & = & \color{red}{1287x} +110 \\\Leftrightarrow & 572x \color{red}{+39} \color{blue}{-39} \color{blue}{-1287x} & = & \color{red}{1287x} +110 \color{blue}{-1287x} \color{blue}{-39} \\\Leftrightarrow & 572x-1287x& = & 110-39 \\\Leftrightarrow & \color{red}{-715} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-715} & & \\\Leftrightarrow & x = \frac{-71}{715} & & \\ & V = \left\{ \frac{-71}{715} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(-4x+\frac{8}{9})& = & (-3x+\frac{2}{3}). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+8} & = & \color{red}{-27x} +6 \\\Leftrightarrow & -36x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +6 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & -36x+27x& = & 6-8 \\\Leftrightarrow & \color{red}{-9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-9} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{14})& = & 9x+\frac{6}{13} \\\Leftrightarrow & -14x+\frac{5}{2}& = & 9x+\frac{6}{13} \\ & & & \text{kgv van noemers 2 en 13 is 26} \\\Leftrightarrow & \color{blue}{26} .(-14x+\frac{5}{2})& = & (9x+\frac{6}{13}). \color{blue}{26} \\\Leftrightarrow & -364x \color{red}{+65} & = & \color{red}{234x} +12 \\\Leftrightarrow & -364x \color{red}{+65} \color{blue}{-65} \color{blue}{-234x} & = & \color{red}{234x} +12 \color{blue}{-234x} \color{blue}{-65} \\\Leftrightarrow & -364x-234x& = & 12-65 \\\Leftrightarrow & \color{red}{-598} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-598} & & \\\Leftrightarrow & x = \frac{53}{598} & & \\ & V = \left\{ \frac{53}{598} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{9})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 25x+\frac{10}{9}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(25x+\frac{10}{9})& = & (7x+\frac{10}{9}). \color{blue}{9} \\\Leftrightarrow & 225x \color{red}{+10} & = & \color{red}{63x} +10 \\\Leftrightarrow & 225x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & 225x-63x& = & 10-10 \\\Leftrightarrow & \color{red}{162} x& = & 0 \\\Leftrightarrow & x = \frac{0}{162} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-x+\frac{5}{7})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -3x+\frac{15}{7}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(-3x+\frac{15}{7})& = & (-5x+\frac{9}{8}). \color{blue}{56} \\\Leftrightarrow & -168x \color{red}{+120} & = & \color{red}{-280x} +63 \\\Leftrightarrow & -168x \color{red}{+120} \color{blue}{-120} \color{blue}{+280x} & = & \color{red}{-280x} +63 \color{blue}{+280x} \color{blue}{-120} \\\Leftrightarrow & -168x+280x& = & 63-120 \\\Leftrightarrow & \color{red}{112} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{112} & & \\ & V = \left\{ \frac{-57}{112} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{11})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -14x+\frac{28}{11}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(-14x+\frac{28}{11})& = & (3x+\frac{2}{9}). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+252} & = & \color{red}{297x} +22 \\\Leftrightarrow & -1386x \color{red}{+252} \color{blue}{-252} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{-252} \\\Leftrightarrow & -1386x-297x& = & 22-252 \\\Leftrightarrow & \color{red}{-1683} x& = & -230 \\\Leftrightarrow & x = \frac{-230}{-1683} & & \\\Leftrightarrow & x = \frac{230}{1683} & & \\ & V = \left\{ \frac{230}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{9})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -6x-\frac{4}{3}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(-6x-\frac{4}{3})& = & (7x+\frac{6}{7}). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{147x} +18 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{-147x} & = & \color{red}{147x} +18 \color{blue}{-147x} \color{blue}{+28} \\\Leftrightarrow & -126x-147x& = & 18+28 \\\Leftrightarrow & \color{red}{-273} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-273} & & \\\Leftrightarrow & x = \frac{-46}{273} & & \\ & V = \left\{ \frac{-46}{273} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & -4x+\frac{4}{7} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(-25x+\frac{20}{7})& = & (-4x+\frac{4}{7}). \color{blue}{7} \\\Leftrightarrow & -175x \color{red}{+20} & = & \color{red}{-28x} +4 \\\Leftrightarrow & -175x \color{red}{+20} \color{blue}{-20} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-20} \\\Leftrightarrow & -175x+28x& = & 4-20 \\\Leftrightarrow & \color{red}{-147} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-147} & & \\\Leftrightarrow & x = \frac{16}{147} & & \\ & V = \left\{ \frac{16}{147} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-x-\frac{4}{5})& = & -8x+\frac{3}{7} \\\Leftrightarrow & 3x+\frac{12}{5}& = & -8x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(3x+\frac{12}{5})& = & (-8x+\frac{3}{7}). \color{blue}{35} \\\Leftrightarrow & 105x \color{red}{+84} & = & \color{red}{-280x} +15 \\\Leftrightarrow & 105x \color{red}{+84} \color{blue}{-84} \color{blue}{+280x} & = & \color{red}{-280x} +15 \color{blue}{+280x} \color{blue}{-84} \\\Leftrightarrow & 105x+280x& = & 15-84 \\\Leftrightarrow & \color{red}{385} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{385} & & \\ & V = \left\{ \frac{-69}{385} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (2x-\frac{2}{13})& = & 3x+\frac{7}{12} \\\Leftrightarrow & 2x-\frac{2}{13}& = & 3x+\frac{7}{12} \\ & & & \text{kgv van noemers 13 en 12 is 156} \\\Leftrightarrow & \color{blue}{156} .(2x-\frac{2}{13})& = & (3x+\frac{7}{12}). \color{blue}{156} \\\Leftrightarrow & 312x \color{red}{-24} & = & \color{red}{468x} +91 \\\Leftrightarrow & 312x \color{red}{-24} \color{blue}{+24} \color{blue}{-468x} & = & \color{red}{468x} +91 \color{blue}{-468x} \color{blue}{+24} \\\Leftrightarrow & 312x-468x& = & 91+24 \\\Leftrightarrow & \color{red}{-156} x& = & 115 \\\Leftrightarrow & x = \frac{115}{-156} & & \\\Leftrightarrow & x = \frac{-115}{156} & & \\ & V = \left\{ \frac{-115}{156} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & 7x+\frac{3}{13} \\\Leftrightarrow & -15x-\frac{20}{9}& = & 7x+\frac{3}{13} \\ & & & \text{kgv van noemers 9 en 13 is 117} \\\Leftrightarrow & \color{blue}{117} .(-15x-\frac{20}{9})& = & (7x+\frac{3}{13}). \color{blue}{117} \\\Leftrightarrow & -1755x \color{red}{-260} & = & \color{red}{819x} +27 \\\Leftrightarrow & -1755x \color{red}{-260} \color{blue}{+260} \color{blue}{-819x} & = & \color{red}{819x} +27 \color{blue}{-819x} \color{blue}{+260} \\\Leftrightarrow & -1755x-819x& = & 27+260 \\\Leftrightarrow & \color{red}{-2574} x& = & 287 \\\Leftrightarrow & x = \frac{287}{-2574} & & \\\Leftrightarrow & x = \frac{-287}{2574} & & \\ & V = \left\{ \frac{-287}{2574} \right\} & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2025-04-02 04:29:12