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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{11})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x-\frac{10}{11}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{-10} & = & \color{red}{77x} +8 \\\Leftrightarrow & -110x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +8 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & -110x-77x& = & 8+10 \\\Leftrightarrow & \color{red}{-187} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-187} & & \\\Leftrightarrow & x = \frac{-18}{187} & & \\ & V = \left\{ \frac{-18}{187} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 6x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{336}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{-147} & = & \color{red}{336x} +80 \\\Leftrightarrow & -1960x \color{red}{-147} \color{blue}{+147} \color{blue}{-336x} & = & \color{red}{336x} +80 \color{blue}{-336x} \color{blue}{+147} \\\Leftrightarrow & -1960x-336x& = & 80+147 \\\Leftrightarrow & \color{red}{-2296} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-2296} & & \\\Leftrightarrow & x = \frac{-227}{2296} & & \\ & V = \left\{ \frac{-227}{2296} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+30} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 198x \color{red}{+30} \color{blue}{-30} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-30} \\\Leftrightarrow & 198x+165x& = & 44-30 \\\Leftrightarrow & \color{red}{363} x& = & 14 \\\Leftrightarrow & x = \frac{14}{363} & & \\ & V = \left\{ \frac{14}{363} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & 3x+\frac{2}{5} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{175}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-175} & = & \color{red}{165x} +22 \\\Leftrightarrow & 1540x \color{red}{-175} \color{blue}{+175} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+175} \\\Leftrightarrow & 1540x-165x& = & 22+175 \\\Leftrightarrow & \color{red}{1375} x& = & 197 \\\Leftrightarrow & x = \frac{197}{1375} & & \\ & V = \left\{ \frac{197}{1375} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{2}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{+108} & = & \color{red}{315x} +40 \\\Leftrightarrow & 1350x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 1350x-315x& = & 40-108 \\\Leftrightarrow & \color{red}{1035} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{1035} & & \\ & V = \left\{ \frac{-68}{1035} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-150} & = & \color{red}{-245x} +63 \\\Leftrightarrow & -1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & -1050x+245x& = & 63+150 \\\Leftrightarrow & \color{red}{-805} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-805} & & \\\Leftrightarrow & x = \frac{-213}{805} & & \\ & V = \left\{ \frac{-213}{805} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -120x+50x& = & 35+24 \\\Leftrightarrow & \color{red}{-70} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-70} & & \\\Leftrightarrow & x = \frac{-59}{70} & & \\ & V = \left\{ \frac{-59}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{55x} +5 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +5 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & -198x-55x& = & 5+18 \\\Leftrightarrow & \color{red}{-253} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-253} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & -180x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{-105} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-105} & & \\\Leftrightarrow & x = \frac{-4}{105} & & \\ & V = \left\{ \frac{-4}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{9}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x- \frac{9}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{-9} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -99x \color{red}{-9} \color{blue}{+9} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+9} \\\Leftrightarrow & -99x+55x& = & 2+9 \\\Leftrightarrow & \color{red}{-44} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-44} & & \\\Leftrightarrow & x = \frac{-1}{4} & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{4}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 35x-4& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{70}{ \color{blue}{2} }x- \frac{8}{ \color{blue}{2} })& = & (\frac{6}{ \color{blue}{2} }x+ \frac{7}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 70x \color{red}{-8} & = & \color{red}{6x} +7 \\\Leftrightarrow & 70x \color{red}{-8} \color{blue}{+8} \color{blue}{-6x} & = & \color{red}{6x} +7 \color{blue}{-6x} \color{blue}{+8} \\\Leftrightarrow & 70x-6x& = & 7+8 \\\Leftrightarrow & \color{red}{64} x& = & 15 \\\Leftrightarrow & x = \frac{15}{64} & & \\ & V = \left\{ \frac{15}{64} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{4}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x- \frac{20}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{-20} & = & \color{red}{275x} +66 \\\Leftrightarrow & 330x \color{red}{-20} \color{blue}{+20} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{+20} \\\Leftrightarrow & 330x-275x& = & 66+20 \\\Leftrightarrow & \color{red}{55} x& = & 86 \\\Leftrightarrow & x = \frac{86}{55} & & \\ & V = \left\{ \frac{86}{55} \right\} & \\\end{align}\)
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