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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{11})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -20x+\frac{16}{11}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x+ \frac{144}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{+144} & = & \color{red}{-693x} +110 \\\Leftrightarrow & -1980x \color{red}{+144} \color{blue}{-144} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-144} \\\Leftrightarrow & -1980x+693x& = & 110-144 \\\Leftrightarrow & \color{red}{-1287} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-1287} & & \\\Leftrightarrow & x = \frac{34}{1287} & & \\ & V = \left\{ \frac{34}{1287} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{7})& = & 4x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{15}{7}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{75}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+75} & = & \color{red}{140x} +49 \\\Leftrightarrow & 525x \color{red}{+75} \color{blue}{-75} \color{blue}{-140x} & = & \color{red}{140x} +49 \color{blue}{-140x} \color{blue}{-75} \\\Leftrightarrow & 525x-140x& = & 49-75 \\\Leftrightarrow & \color{red}{385} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{385} & & \\ & V = \left\{ \frac{-26}{385} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & 16x+\frac{8}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1152}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1152x \color{red}{+64} & = & \color{red}{-216x} +63 \\\Leftrightarrow & 1152x \color{red}{+64} \color{blue}{-64} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{-64} \\\Leftrightarrow & 1152x+216x& = & 63-64 \\\Leftrightarrow & \color{red}{1368} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{1368} & & \\ & V = \left\{ \frac{-1}{1368} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{4})& = & -4x+\frac{5}{8} \\\Leftrightarrow & -25x-\frac{25}{4}& = & -4x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{50}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-50} & = & \color{red}{-32x} +5 \\\Leftrightarrow & -200x \color{red}{-50} \color{blue}{+50} \color{blue}{+32x} & = & \color{red}{-32x} +5 \color{blue}{+32x} \color{blue}{+50} \\\Leftrightarrow & -200x+32x& = & 5+50 \\\Leftrightarrow & \color{red}{-168} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-168} & & \\\Leftrightarrow & x = \frac{-55}{168} & & \\ & V = \left\{ \frac{-55}{168} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{2})& = & 6x+\frac{5}{3} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 6x+\frac{5}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x- \frac{75}{ \color{blue}{6} })& = & (\frac{36}{ \color{blue}{6} }x+ \frac{10}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{-75} & = & \color{red}{36x} +10 \\\Leftrightarrow & 150x \color{red}{-75} \color{blue}{+75} \color{blue}{-36x} & = & \color{red}{36x} +10 \color{blue}{-36x} \color{blue}{+75} \\\Leftrightarrow & 150x-36x& = & 10+75 \\\Leftrightarrow & \color{red}{114} x& = & 85 \\\Leftrightarrow & x = \frac{85}{114} & & \\ & V = \left\{ \frac{85}{114} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{6})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 25x-\frac{25}{6}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1050}{ \color{blue}{42} }x- \frac{175}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1050x \color{red}{-175} & = & \color{red}{-378x} +48 \\\Leftrightarrow & 1050x \color{red}{-175} \color{blue}{+175} \color{blue}{+378x} & = & \color{red}{-378x} +48 \color{blue}{+378x} \color{blue}{+175} \\\Leftrightarrow & 1050x+378x& = & 48+175 \\\Leftrightarrow & \color{red}{1428} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1428} & & \\ & V = \left\{ \frac{223}{1428} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 5x+\frac{5}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{105x} +35 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +35 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 126x-105x& = & 35+18 \\\Leftrightarrow & \color{red}{21} x& = & 53 \\\Leftrightarrow & x = \frac{53}{21} & & \\ & V = \left\{ \frac{53}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -16x-\frac{16}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-48} & = & \color{red}{231x} +22 \\\Leftrightarrow & -528x \color{red}{-48} \color{blue}{+48} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+48} \\\Leftrightarrow & -528x-231x& = & 22+48 \\\Leftrightarrow & \color{red}{-759} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-759} & & \\\Leftrightarrow & x = \frac{-70}{759} & & \\ & V = \left\{ \frac{-70}{759} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{4})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{-196x} +40 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +40 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & -280x+196x& = & 40-105 \\\Leftrightarrow & \color{red}{-84} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{-84} & & \\\Leftrightarrow & x = \frac{65}{84} & & \\ & V = \left\{ \frac{65}{84} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{11})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{21}{11}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{147}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-147} & = & \color{red}{-693x} +33 \\\Leftrightarrow & 1078x \color{red}{-147} \color{blue}{+147} \color{blue}{+693x} & = & \color{red}{-693x} +33 \color{blue}{+693x} \color{blue}{+147} \\\Leftrightarrow & 1078x+693x& = & 33+147 \\\Leftrightarrow & \color{red}{1771} x& = & 180 \\\Leftrightarrow & x = \frac{180}{1771} & & \\ & V = \left\{ \frac{180}{1771} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{-18} & = & \color{red}{77x} +10 \\\Leftrightarrow & 330x \color{red}{-18} \color{blue}{+18} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{+18} \\\Leftrightarrow & 330x-77x& = & 10+18 \\\Leftrightarrow & \color{red}{253} x& = & 28 \\\Leftrightarrow & x = \frac{28}{253} & & \\ & V = \left\{ \frac{28}{253} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+90} & = & \color{red}{-147x} +49 \\\Leftrightarrow & -630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +49 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & -630x+147x& = & 49-90 \\\Leftrightarrow & \color{red}{-483} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-483} & & \\\Leftrightarrow & x = \frac{41}{483} & & \\ & V = \left\{ \frac{41}{483} \right\} & \\\end{align}\)
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