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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{126}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 126x \color{red}{-30} & = & \color{red}{49x} +9 \\\Leftrightarrow & 126x \color{red}{-30} \color{blue}{+30} \color{blue}{-49x} & = & \color{red}{49x} +9 \color{blue}{-49x} \color{blue}{+30} \\\Leftrightarrow & 126x-49x& = & 9+30 \\\Leftrightarrow & \color{red}{77} x& = & 39 \\\Leftrightarrow & x = \frac{39}{77} & & \\ & V = \left\{ \frac{39}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{567x} +70 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-567x} & = & \color{red}{567x} +70 \color{blue}{-567x} \color{blue}{+180} \\\Leftrightarrow & -1260x-567x& = & 70+180 \\\Leftrightarrow & \color{red}{-1827} x& = & 250 \\\Leftrightarrow & x = \frac{250}{-1827} & & \\\Leftrightarrow & x = \frac{-250}{1827} & & \\ & V = \left\{ \frac{-250}{1827} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{385x} +35 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +35 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1848x-385x& = & 35+330 \\\Leftrightarrow & \color{red}{1463} x& = & 365 \\\Leftrightarrow & x = \frac{365}{1463} & & \\ & V = \left\{ \frac{365}{1463} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{960}{ \color{blue}{60} }x- \frac{144}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 960x \color{red}{-144} & = & \color{red}{-300x} +35 \\\Leftrightarrow & 960x \color{red}{-144} \color{blue}{+144} \color{blue}{+300x} & = & \color{red}{-300x} +35 \color{blue}{+300x} \color{blue}{+144} \\\Leftrightarrow & 960x+300x& = & 35+144 \\\Leftrightarrow & \color{red}{1260} x& = & 179 \\\Leftrightarrow & x = \frac{179}{1260} & & \\ & V = \left\{ \frac{179}{1260} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{11})& = & 9x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+150} & = & \color{red}{495x} +22 \\\Leftrightarrow & -990x \color{red}{+150} \color{blue}{-150} \color{blue}{-495x} & = & \color{red}{495x} +22 \color{blue}{-495x} \color{blue}{-150} \\\Leftrightarrow & -990x-495x& = & 22-150 \\\Leftrightarrow & \color{red}{-1485} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-1485} & & \\\Leftrightarrow & x = \frac{128}{1485} & & \\ & V = \left\{ \frac{128}{1485} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{9})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{4}{9}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+4} & = & \color{red}{-27x} +30 \\\Leftrightarrow & -72x \color{red}{+4} \color{blue}{-4} \color{blue}{+27x} & = & \color{red}{-27x} +30 \color{blue}{+27x} \color{blue}{-4} \\\Leftrightarrow & -72x+27x& = & 30-4 \\\Leftrightarrow & \color{red}{-45} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-45} & & \\\Leftrightarrow & x = \frac{-26}{45} & & \\ & V = \left\{ \frac{-26}{45} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{2})& = & -2x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{25}{2}& = & -2x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{275}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+275} & = & \color{red}{-44x} +4 \\\Leftrightarrow & 330x \color{red}{+275} \color{blue}{-275} \color{blue}{+44x} & = & \color{red}{-44x} +4 \color{blue}{+44x} \color{blue}{-275} \\\Leftrightarrow & 330x+44x& = & 4-275 \\\Leftrightarrow & \color{red}{374} x& = & -271 \\\Leftrightarrow & x = \frac{-271}{374} & & \\ & V = \left\{ \frac{-271}{374} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{-105x} +15 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{-28} \\\Leftrightarrow & 350x+105x& = & 15-28 \\\Leftrightarrow & \color{red}{455} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{455} & & \\\Leftrightarrow & x = \frac{-1}{35} & & \\ & V = \left\{ \frac{-1}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{8}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+16} & = & \color{red}{-50x} +25 \\\Leftrightarrow & 120x \color{red}{+16} \color{blue}{-16} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-16} \\\Leftrightarrow & 120x+50x& = & 25-16 \\\Leftrightarrow & \color{red}{170} x& = & 9 \\\Leftrightarrow & x = \frac{9}{170} & & \\ & V = \left\{ \frac{9}{170} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -8x+\frac{10}{11} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -8x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x+ \frac{231}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{+231} & = & \color{red}{-176x} +20 \\\Leftrightarrow & 462x \color{red}{+231} \color{blue}{-231} \color{blue}{+176x} & = & \color{red}{-176x} +20 \color{blue}{+176x} \color{blue}{-231} \\\Leftrightarrow & 462x+176x& = & 20-231 \\\Leftrightarrow & \color{red}{638} x& = & -211 \\\Leftrightarrow & x = \frac{-211}{638} & & \\ & V = \left\{ \frac{-211}{638} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{7})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+6} & = & \color{red}{35x} +4 \\\Leftrightarrow & -28x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & -28x-35x& = & 4-6 \\\Leftrightarrow & \color{red}{-63} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-63} & & \\\Leftrightarrow & x = \frac{2}{63} & & \\ & V = \left\{ \frac{2}{63} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -4x-\frac{4}{5}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-44} & = & \color{red}{-495x} +20 \\\Leftrightarrow & -220x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +20 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & -220x+495x& = & 20+44 \\\Leftrightarrow & \color{red}{275} x& = & 64 \\\Leftrightarrow & x = \frac{64}{275} & & \\ & V = \left\{ \frac{64}{275} \right\} & \\\end{align}\)
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