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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -9x+\frac{6}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+42} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -693x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & -693x+385x& = & 22-42 \\\Leftrightarrow & \color{red}{-308} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-308} & & \\\Leftrightarrow & x = \frac{5}{77} & & \\ & V = \left\{ \frac{5}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{9})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{8}{9}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-56} & = & \color{red}{189x} +72 \\\Leftrightarrow & 504x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +72 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & 504x-189x& = & 72+56 \\\Leftrightarrow & \color{red}{315} x& = & 128 \\\Leftrightarrow & x = \frac{128}{315} & & \\ & V = \left\{ \frac{128}{315} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{18}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-18} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -150x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & -150x+35x& = & 6+18 \\\Leftrightarrow & \color{red}{-115} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-115} & & \\\Leftrightarrow & x = \frac{-24}{115} & & \\ & V = \left\{ \frac{-24}{115} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & 630x+441x& = & 14+90 \\\Leftrightarrow & \color{red}{1071} x& = & 104 \\\Leftrightarrow & x = \frac{104}{1071} & & \\ & V = \left\{ \frac{104}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & 9x+\frac{10}{3} \\\Leftrightarrow & -25x+\frac{10}{7}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -525x \color{red}{+30} & = & \color{red}{189x} +70 \\\Leftrightarrow & -525x \color{red}{+30} \color{blue}{-30} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{-30} \\\Leftrightarrow & -525x-189x& = & 70-30 \\\Leftrightarrow & \color{red}{-714} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-714} & & \\\Leftrightarrow & x = \frac{-20}{357} & & \\ & V = \left\{ \frac{-20}{357} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{4})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -35x+\frac{35}{4}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{105}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-36x} +8 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+36x} & = & \color{red}{-36x} +8 \color{blue}{+36x} \color{blue}{-105} \\\Leftrightarrow & -420x+36x& = & 8-105 \\\Leftrightarrow & \color{red}{-384} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-384} & & \\\Leftrightarrow & x = \frac{97}{384} & & \\ & V = \left\{ \frac{97}{384} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-36} \\\Leftrightarrow & 180x+50x& = & 15-36 \\\Leftrightarrow & \color{red}{230} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{230} & & \\ & V = \left\{ \frac{-21}{230} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{2}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{275x} +22 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +22 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & -1320x-275x& = & 22+90 \\\Leftrightarrow & \color{red}{-1595} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-1595} & & \\\Leftrightarrow & x = \frac{-112}{1595} & & \\ & V = \left\{ \frac{-112}{1595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 20x-\frac{15}{8}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{-165} & = & \color{red}{616x} +16 \\\Leftrightarrow & 1760x \color{red}{-165} \color{blue}{+165} \color{blue}{-616x} & = & \color{red}{616x} +16 \color{blue}{-616x} \color{blue}{+165} \\\Leftrightarrow & 1760x-616x& = & 16+165 \\\Leftrightarrow & \color{red}{1144} x& = & 181 \\\Leftrightarrow & x = \frac{181}{1144} & & \\ & V = \left\{ \frac{181}{1144} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{245x} +28 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+150} \\\Leftrightarrow & -840x-245x& = & 28+150 \\\Leftrightarrow & \color{red}{-1085} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1085} & & \\\Leftrightarrow & x = \frac{-178}{1085} & & \\ & V = \left\{ \frac{-178}{1085} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+220} & = & \color{red}{891x} +54 \\\Leftrightarrow & 1980x \color{red}{+220} \color{blue}{-220} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{-220} \\\Leftrightarrow & 1980x-891x& = & 54-220 \\\Leftrightarrow & \color{red}{1089} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{1089} & & \\ & V = \left\{ \frac{-166}{1089} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{5})& = & 3x+\frac{3}{5} \\\Leftrightarrow & -14x+\frac{28}{5}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-70}{ \color{blue}{5} }x+ \frac{28}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -70x \color{red}{+28} & = & \color{red}{15x} +3 \\\Leftrightarrow & -70x \color{red}{+28} \color{blue}{-28} \color{blue}{-15x} & = & \color{red}{15x} +3 \color{blue}{-15x} \color{blue}{-28} \\\Leftrightarrow & -70x-15x& = & 3-28 \\\Leftrightarrow & \color{red}{-85} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-85} & & \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
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