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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{11})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{+147} & = & \color{red}{-693x} +110 \\\Leftrightarrow & 1078x \color{red}{+147} \color{blue}{-147} \color{blue}{+693x} & = & \color{red}{-693x} +110 \color{blue}{+693x} \color{blue}{-147} \\\Leftrightarrow & 1078x+693x& = & 110-147 \\\Leftrightarrow & \color{red}{1771} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{1771} & & \\ & V = \left\{ \frac{-37}{1771} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{3})& = & 6x+\frac{10}{3} \\\Leftrightarrow & -35x-\frac{28}{3}& = & 6x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{18}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-28} & = & \color{red}{18x} +10 \\\Leftrightarrow & -105x \color{red}{-28} \color{blue}{+28} \color{blue}{-18x} & = & \color{red}{18x} +10 \color{blue}{-18x} \color{blue}{+28} \\\Leftrightarrow & -105x-18x& = & 10+28 \\\Leftrightarrow & \color{red}{-123} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-123} & & \\\Leftrightarrow & x = \frac{-38}{123} & & \\ & V = \left\{ \frac{-38}{123} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{4}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{8}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-8} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -140x \color{red}{-8} \color{blue}{+8} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+8} \\\Leftrightarrow & -140x+98x& = & 35+8 \\\Leftrightarrow & \color{red}{-42} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-42} & & \\\Leftrightarrow & x = \frac{-43}{42} & & \\ & V = \left\{ \frac{-43}{42} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-50} & = & \color{red}{-245x} +21 \\\Leftrightarrow & 350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +21 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & 350x+245x& = & 21+50 \\\Leftrightarrow & \color{red}{595} x& = & 71 \\\Leftrightarrow & x = \frac{71}{595} & & \\ & V = \left\{ \frac{71}{595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{11})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+18} & = & \color{red}{-55x} +6 \\\Leftrightarrow & 132x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +6 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & 132x+55x& = & 6-18 \\\Leftrightarrow & \color{red}{187} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{187} & & \\ & V = \left\{ \frac{-12}{187} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 18x-\frac{18}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{-55x} +4 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 198x+55x& = & 4+18 \\\Leftrightarrow & \color{red}{253} x& = & 22 \\\Leftrightarrow & x = \frac{22}{253} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{3})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+88} & = & \color{red}{297x} +30 \\\Leftrightarrow & -264x \color{red}{+88} \color{blue}{-88} \color{blue}{-297x} & = & \color{red}{297x} +30 \color{blue}{-297x} \color{blue}{-88} \\\Leftrightarrow & -264x-297x& = & 30-88 \\\Leftrightarrow & \color{red}{-561} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-561} & & \\\Leftrightarrow & x = \frac{58}{561} & & \\ & V = \left\{ \frac{58}{561} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-240}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -240x \color{red}{-24} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -240x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -240x+50x& = & 15+24 \\\Leftrightarrow & \color{red}{-190} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-190} & & \\\Leftrightarrow & x = \frac{-39}{190} & & \\ & V = \left\{ \frac{-39}{190} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-44} & = & \color{red}{-495x} +18 \\\Leftrightarrow & 594x \color{red}{-44} \color{blue}{+44} \color{blue}{+495x} & = & \color{red}{-495x} +18 \color{blue}{+495x} \color{blue}{+44} \\\Leftrightarrow & 594x+495x& = & 18+44 \\\Leftrightarrow & \color{red}{1089} x& = & 62 \\\Leftrightarrow & x = \frac{62}{1089} & & \\ & V = \left\{ \frac{62}{1089} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{9})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{4}{9}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-4} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -54x \color{red}{-4} \color{blue}{+4} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{+4} \\\Leftrightarrow & -54x+63x& = & 10+4 \\\Leftrightarrow & \color{red}{9} x& = & 14 \\\Leftrightarrow & x = \frac{14}{9} & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{24}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{48}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+48} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -168x \color{red}{+48} \color{blue}{-48} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-48} \\\Leftrightarrow & -168x+70x& = & 63-48 \\\Leftrightarrow & \color{red}{-98} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-98} & & \\\Leftrightarrow & x = \frac{-15}{98} & & \\ & V = \left\{ \frac{-15}{98} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +35 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +35 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 35-36 \\\Leftrightarrow & \color{red}{-255} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-255} & & \\\Leftrightarrow & x = \frac{1}{255} & & \\ & V = \left\{ \frac{1}{255} \right\} & \\\end{align}\)
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