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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{11})& = & -3x+\frac{7}{6} \\\Leftrightarrow & -28x+\frac{14}{11}& = & -3x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1848}{ \color{blue}{66} }x+ \frac{84}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1848x \color{red}{+84} & = & \color{red}{-198x} +77 \\\Leftrightarrow & -1848x \color{red}{+84} \color{blue}{-84} \color{blue}{+198x} & = & \color{red}{-198x} +77 \color{blue}{+198x} \color{blue}{-84} \\\Leftrightarrow & -1848x+198x& = & 77-84 \\\Leftrightarrow & \color{red}{-1650} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-1650} & & \\\Leftrightarrow & x = \frac{7}{1650} & & \\ & V = \left\{ \frac{7}{1650} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{3})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{35}{3}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+385} & = & \color{red}{-66x} +18 \\\Leftrightarrow & 1155x \color{red}{+385} \color{blue}{-385} \color{blue}{+66x} & = & \color{red}{-66x} +18 \color{blue}{+66x} \color{blue}{-385} \\\Leftrightarrow & 1155x+66x& = & 18-385 \\\Leftrightarrow & \color{red}{1221} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{1221} & & \\ & V = \left\{ \frac{-367}{1221} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{11})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -10x+\frac{8}{11}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-880}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -880x \color{red}{+64} & = & \color{red}{616x} +55 \\\Leftrightarrow & -880x \color{red}{+64} \color{blue}{-64} \color{blue}{-616x} & = & \color{red}{616x} +55 \color{blue}{-616x} \color{blue}{-64} \\\Leftrightarrow & -880x-616x& = & 55-64 \\\Leftrightarrow & \color{red}{-1496} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-1496} & & \\\Leftrightarrow & x = \frac{9}{1496} & & \\ & V = \left\{ \frac{9}{1496} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{8})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{-15} & = & \color{red}{56x} +14 \\\Leftrightarrow & 120x \color{red}{-15} \color{blue}{+15} \color{blue}{-56x} & = & \color{red}{56x} +14 \color{blue}{-56x} \color{blue}{+15} \\\Leftrightarrow & 120x-56x& = & 14+15 \\\Leftrightarrow & \color{red}{64} x& = & 29 \\\Leftrightarrow & x = \frac{29}{64} & & \\ & V = \left\{ \frac{29}{64} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{7})& = & 3x+\frac{8}{7} \\\Leftrightarrow & -35x-4& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-245}{ \color{blue}{7} }x- \frac{28}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -245x \color{red}{-28} & = & \color{red}{21x} +8 \\\Leftrightarrow & -245x \color{red}{-28} \color{blue}{+28} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+28} \\\Leftrightarrow & -245x-21x& = & 8+28 \\\Leftrightarrow & \color{red}{-266} x& = & 36 \\\Leftrightarrow & x = \frac{36}{-266} & & \\\Leftrightarrow & x = \frac{-18}{133} & & \\ & V = \left\{ \frac{-18}{133} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{5}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 24x+\frac{30}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+120} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 1056x \color{red}{+120} \color{blue}{-120} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{-120} \\\Leftrightarrow & 1056x+220x& = & 99-120 \\\Leftrightarrow & \color{red}{1276} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{1276} & & \\ & V = \left\{ \frac{-21}{1276} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -120x+50x& = & 35+24 \\\Leftrightarrow & \color{red}{-70} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-70} & & \\\Leftrightarrow & x = \frac{-59}{70} & & \\ & V = \left\{ \frac{-59}{70} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{30}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-150} & = & \color{red}{385x} +66 \\\Leftrightarrow & 1650x \color{red}{-150} \color{blue}{+150} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+150} \\\Leftrightarrow & 1650x-385x& = & 66+150 \\\Leftrightarrow & \color{red}{1265} x& = & 216 \\\Leftrightarrow & x = \frac{216}{1265} & & \\ & V = \left\{ \frac{216}{1265} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{6})& = & 6x+\frac{4}{7} \\\Leftrightarrow & -28x-\frac{35}{6}& = & 6x+\frac{4}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1176}{ \color{blue}{42} }x- \frac{245}{ \color{blue}{42} })& = & (\frac{252}{ \color{blue}{42} }x+ \frac{24}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1176x \color{red}{-245} & = & \color{red}{252x} +24 \\\Leftrightarrow & -1176x \color{red}{-245} \color{blue}{+245} \color{blue}{-252x} & = & \color{red}{252x} +24 \color{blue}{-252x} \color{blue}{+245} \\\Leftrightarrow & -1176x-252x& = & 24+245 \\\Leftrightarrow & \color{red}{-1428} x& = & 269 \\\Leftrightarrow & x = \frac{269}{-1428} & & \\\Leftrightarrow & x = \frac{-269}{1428} & & \\ & V = \left\{ \frac{-269}{1428} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{11})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 28x+\frac{28}{11}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2156}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2156x \color{red}{+196} & = & \color{red}{231x} +66 \\\Leftrightarrow & 2156x \color{red}{+196} \color{blue}{-196} \color{blue}{-231x} & = & \color{red}{231x} +66 \color{blue}{-231x} \color{blue}{-196} \\\Leftrightarrow & 2156x-231x& = & 66-196 \\\Leftrightarrow & \color{red}{1925} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{1925} & & \\\Leftrightarrow & x = \frac{-26}{385} & & \\ & V = \left\{ \frac{-26}{385} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{9})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{8}{9}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+8} & = & \color{red}{-63x} +24 \\\Leftrightarrow & 72x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 72x+63x& = & 24-8 \\\Leftrightarrow & \color{red}{135} x& = & 16 \\\Leftrightarrow & x = \frac{16}{135} & & \\ & V = \left\{ \frac{16}{135} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{11})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 12x+\frac{20}{11}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1584}{ \color{blue}{132} }x+ \frac{240}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1584x \color{red}{+240} & = & \color{red}{-924x} +55 \\\Leftrightarrow & 1584x \color{red}{+240} \color{blue}{-240} \color{blue}{+924x} & = & \color{red}{-924x} +55 \color{blue}{+924x} \color{blue}{-240} \\\Leftrightarrow & 1584x+924x& = & 55-240 \\\Leftrightarrow & \color{red}{2508} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{2508} & & \\ & V = \left\{ \frac{-185}{2508} \right\} & \\\end{align}\)
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