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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{15}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-45} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 198x \color{red}{-45} \color{blue}{+45} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+45} \\\Leftrightarrow & 198x+165x& = & 22+45 \\\Leftrightarrow & \color{red}{363} x& = & 67 \\\Leftrightarrow & x = \frac{67}{363} & & \\ & V = \left\{ \frac{67}{363} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{5}{7})& = & 5x+\frac{5}{9} \\\Leftrightarrow & -9x+\frac{15}{7}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{+135} & = & \color{red}{315x} +35 \\\Leftrightarrow & -567x \color{red}{+135} \color{blue}{-135} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{-135} \\\Leftrightarrow & -567x-315x& = & 35-135 \\\Leftrightarrow & \color{red}{-882} x& = & -100 \\\Leftrightarrow & x = \frac{-100}{-882} & & \\\Leftrightarrow & x = \frac{50}{441} & & \\ & V = \left\{ \frac{50}{441} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{11})& = & 6x+\frac{9}{4} \\\Leftrightarrow & -18x+\frac{24}{11}& = & 6x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-792}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -792x \color{red}{+96} & = & \color{red}{264x} +99 \\\Leftrightarrow & -792x \color{red}{+96} \color{blue}{-96} \color{blue}{-264x} & = & \color{red}{264x} +99 \color{blue}{-264x} \color{blue}{-96} \\\Leftrightarrow & -792x-264x& = & 99-96 \\\Leftrightarrow & \color{red}{-1056} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-1056} & & \\\Leftrightarrow & x = \frac{-1}{352} & & \\ & V = \left\{ \frac{-1}{352} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & -2x+\frac{3}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & -2x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-112}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{-112x} +24 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{+112x} & = & \color{red}{-112x} +24 \color{blue}{+112x} \color{blue}{+147} \\\Leftrightarrow & 1176x+112x& = & 24+147 \\\Leftrightarrow & \color{red}{1288} x& = & 171 \\\Leftrightarrow & x = \frac{171}{1288} & & \\ & V = \left\{ \frac{171}{1288} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 4x-\frac{4}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-44} & = & \color{red}{-693x} +45 \\\Leftrightarrow & 396x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & 396x+693x& = & 45+44 \\\Leftrightarrow & \color{red}{1089} x& = & 89 \\\Leftrightarrow & x = \frac{89}{1089} & & \\ & V = \left\{ \frac{89}{1089} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & 8x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 8x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+220} & = & \color{red}{616x} +14 \\\Leftrightarrow & -1155x \color{red}{+220} \color{blue}{-220} \color{blue}{-616x} & = & \color{red}{616x} +14 \color{blue}{-616x} \color{blue}{-220} \\\Leftrightarrow & -1155x-616x& = & 14-220 \\\Leftrightarrow & \color{red}{-1771} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{-1771} & & \\\Leftrightarrow & x = \frac{206}{1771} & & \\ & V = \left\{ \frac{206}{1771} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{-36} & = & \color{red}{105x} +10 \\\Leftrightarrow & 225x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 225x-105x& = & 10+36 \\\Leftrightarrow & \color{red}{120} x& = & 46 \\\Leftrightarrow & x = \frac{46}{120} & & \\\Leftrightarrow & x = \frac{23}{60} & & \\ & V = \left\{ \frac{23}{60} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{11})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 28x-\frac{35}{11}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x- \frac{140}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{-140} & = & \color{red}{-132x} +99 \\\Leftrightarrow & 1232x \color{red}{-140} \color{blue}{+140} \color{blue}{+132x} & = & \color{red}{-132x} +99 \color{blue}{+132x} \color{blue}{+140} \\\Leftrightarrow & 1232x+132x& = & 99+140 \\\Leftrightarrow & \color{red}{1364} x& = & 239 \\\Leftrightarrow & x = \frac{239}{1364} & & \\ & V = \left\{ \frac{239}{1364} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-240}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -240x \color{red}{+200} & = & \color{red}{-270x} +9 \\\Leftrightarrow & -240x \color{red}{+200} \color{blue}{-200} \color{blue}{+270x} & = & \color{red}{-270x} +9 \color{blue}{+270x} \color{blue}{-200} \\\Leftrightarrow & -240x+270x& = & 9-200 \\\Leftrightarrow & \color{red}{30} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{30} & & \\ & V = \left\{ \frac{-191}{30} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-25x} +4 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & -60x+25x& = & 4-12 \\\Leftrightarrow & \color{red}{-35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-35} & & \\\Leftrightarrow & x = \frac{8}{35} & & \\ & V = \left\{ \frac{8}{35} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{105x} +70 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 126x-105x& = & 70+18 \\\Leftrightarrow & \color{red}{21} x& = & 88 \\\Leftrightarrow & x = \frac{88}{21} & & \\ & V = \left\{ \frac{88}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{7})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{20}{7}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-180} & = & \color{red}{189x} +56 \\\Leftrightarrow & -1260x \color{red}{-180} \color{blue}{+180} \color{blue}{-189x} & = & \color{red}{189x} +56 \color{blue}{-189x} \color{blue}{+180} \\\Leftrightarrow & -1260x-189x& = & 56+180 \\\Leftrightarrow & \color{red}{-1449} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1449} & & \\\Leftrightarrow & x = \frac{-236}{1449} & & \\ & V = \left\{ \frac{-236}{1449} \right\} & \\\end{align}\)
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