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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{4})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{9}{4}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+99} & = & \color{red}{-308x} +32 \\\Leftrightarrow & -264x \color{red}{+99} \color{blue}{-99} \color{blue}{+308x} & = & \color{red}{-308x} +32 \color{blue}{+308x} \color{blue}{-99} \\\Leftrightarrow & -264x+308x& = & 32-99 \\\Leftrightarrow & \color{red}{44} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{44} & & \\ & V = \left\{ \frac{-67}{44} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{9})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{20}{9}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-80} & = & \color{red}{-252x} +27 \\\Leftrightarrow & -720x \color{red}{-80} \color{blue}{+80} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{+80} \\\Leftrightarrow & -720x+252x& = & 27+80 \\\Leftrightarrow & \color{red}{-468} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-468} & & \\\Leftrightarrow & x = \frac{-107}{468} & & \\ & V = \left\{ \frac{-107}{468} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-84} & = & \color{red}{245x} +40 \\\Leftrightarrow & -1050x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & -1050x-245x& = & 40+84 \\\Leftrightarrow & \color{red}{-1295} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-1295} & & \\\Leftrightarrow & x = \frac{-124}{1295} & & \\ & V = \left\{ \frac{-124}{1295} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{7})& = & 8x+\frac{8}{9} \\\Leftrightarrow & 25x-\frac{25}{7}& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1575}{ \color{blue}{63} }x- \frac{225}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1575x \color{red}{-225} & = & \color{red}{504x} +56 \\\Leftrightarrow & 1575x \color{red}{-225} \color{blue}{+225} \color{blue}{-504x} & = & \color{red}{504x} +56 \color{blue}{-504x} \color{blue}{+225} \\\Leftrightarrow & 1575x-504x& = & 56+225 \\\Leftrightarrow & \color{red}{1071} x& = & 281 \\\Leftrightarrow & x = \frac{281}{1071} & & \\ & V = \left\{ \frac{281}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{12})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{25}{12}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+25} & = & \color{red}{84x} +9 \\\Leftrightarrow & -120x \color{red}{+25} \color{blue}{-25} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{-25} \\\Leftrightarrow & -120x-84x& = & 9-25 \\\Leftrightarrow & \color{red}{-204} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-204} & & \\\Leftrightarrow & x = \frac{4}{51} & & \\ & V = \left\{ \frac{4}{51} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 28x-\frac{35}{11}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x- \frac{350}{ \color{blue}{110} })& = & (\frac{330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{-350} & = & \color{red}{330x} +99 \\\Leftrightarrow & 3080x \color{red}{-350} \color{blue}{+350} \color{blue}{-330x} & = & \color{red}{330x} +99 \color{blue}{-330x} \color{blue}{+350} \\\Leftrightarrow & 3080x-330x& = & 99+350 \\\Leftrightarrow & \color{red}{2750} x& = & 449 \\\Leftrightarrow & x = \frac{449}{2750} & & \\ & V = \left\{ \frac{449}{2750} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{63x} +10 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+24} \\\Leftrightarrow & -90x-63x& = & 10+24 \\\Leftrightarrow & \color{red}{-153} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-153} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+84} & = & \color{red}{315x} +30 \\\Leftrightarrow & 280x \color{red}{+84} \color{blue}{-84} \color{blue}{-315x} & = & \color{red}{315x} +30 \color{blue}{-315x} \color{blue}{-84} \\\Leftrightarrow & 280x-315x& = & 30-84 \\\Leftrightarrow & \color{red}{-35} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-35} & & \\\Leftrightarrow & x = \frac{54}{35} & & \\ & V = \left\{ \frac{54}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-27} & = & \color{red}{30x} +10 \\\Leftrightarrow & 135x \color{red}{-27} \color{blue}{+27} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{+27} \\\Leftrightarrow & 135x-30x& = & 10+27 \\\Leftrightarrow & \color{red}{105} x& = & 37 \\\Leftrightarrow & x = \frac{37}{105} & & \\ & V = \left\{ \frac{37}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{7})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -25x+\frac{10}{7}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-350}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-112}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -350x \color{red}{+20} & = & \color{red}{-112x} +21 \\\Leftrightarrow & -350x \color{red}{+20} \color{blue}{-20} \color{blue}{+112x} & = & \color{red}{-112x} +21 \color{blue}{+112x} \color{blue}{-20} \\\Leftrightarrow & -350x+112x& = & 21-20 \\\Leftrightarrow & \color{red}{-238} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-238} & & \\\Leftrightarrow & x = \frac{-1}{238} & & \\ & V = \left\{ \frac{-1}{238} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{12})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -14x+\frac{35}{12}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1848}{ \color{blue}{132} }x+ \frac{385}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{60}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1848x \color{red}{+385} & = & \color{red}{660x} +60 \\\Leftrightarrow & -1848x \color{red}{+385} \color{blue}{-385} \color{blue}{-660x} & = & \color{red}{660x} +60 \color{blue}{-660x} \color{blue}{-385} \\\Leftrightarrow & -1848x-660x& = & 60-385 \\\Leftrightarrow & \color{red}{-2508} x& = & -325 \\\Leftrightarrow & x = \frac{-325}{-2508} & & \\\Leftrightarrow & x = \frac{325}{2508} & & \\ & V = \left\{ \frac{325}{2508} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{12})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{25}{12}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{1680}{ \color{blue}{84} }x+ \frac{175}{ \color{blue}{84} })& = & (\frac{-252}{ \color{blue}{84} }x+ \frac{36}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 1680x \color{red}{+175} & = & \color{red}{-252x} +36 \\\Leftrightarrow & 1680x \color{red}{+175} \color{blue}{-175} \color{blue}{+252x} & = & \color{red}{-252x} +36 \color{blue}{+252x} \color{blue}{-175} \\\Leftrightarrow & 1680x+252x& = & 36-175 \\\Leftrightarrow & \color{red}{1932} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{1932} & & \\ & V = \left\{ \frac{-139}{1932} \right\} & \\\end{align}\)
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