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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & 8x+\frac{2}{7} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{168}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+98} & = & \color{red}{168x} +6 \\\Leftrightarrow & -441x \color{red}{+98} \color{blue}{-98} \color{blue}{-168x} & = & \color{red}{168x} +6 \color{blue}{-168x} \color{blue}{-98} \\\Leftrightarrow & -441x-168x& = & 6-98 \\\Leftrightarrow & \color{red}{-609} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-609} & & \\\Leftrightarrow & x = \frac{92}{609} & & \\ & V = \left\{ \frac{92}{609} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 9x+\frac{9}{7} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{+98} & = & \color{red}{189x} +27 \\\Leftrightarrow & 588x \color{red}{+98} \color{blue}{-98} \color{blue}{-189x} & = & \color{red}{189x} +27 \color{blue}{-189x} \color{blue}{-98} \\\Leftrightarrow & 588x-189x& = & 27-98 \\\Leftrightarrow & \color{red}{399} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{399} & & \\ & V = \left\{ \frac{-71}{399} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{11})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{4}{11}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+12} & = & \color{red}{99x} +110 \\\Leftrightarrow & -264x \color{red}{+12} \color{blue}{-12} \color{blue}{-99x} & = & \color{red}{99x} +110 \color{blue}{-99x} \color{blue}{-12} \\\Leftrightarrow & -264x-99x& = & 110-12 \\\Leftrightarrow & \color{red}{-363} x& = & 98 \\\Leftrightarrow & x = \frac{98}{-363} & & \\\Leftrightarrow & x = \frac{-98}{363} & & \\ & V = \left\{ \frac{-98}{363} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -5x+\frac{9}{4} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{-100x} +45 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{+100x} & = & \color{red}{-100x} +45 \color{blue}{+100x} \color{blue}{-48} \\\Leftrightarrow & -180x+100x& = & 45-48 \\\Leftrightarrow & \color{red}{-80} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-80} & & \\\Leftrightarrow & x = \frac{3}{80} & & \\ & V = \left\{ \frac{3}{80} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{2}{11})& = & 6x+\frac{2}{5} \\\Leftrightarrow & -18x+\frac{12}{11}& = & 6x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+60} & = & \color{red}{330x} +22 \\\Leftrightarrow & -990x \color{red}{+60} \color{blue}{-60} \color{blue}{-330x} & = & \color{red}{330x} +22 \color{blue}{-330x} \color{blue}{-60} \\\Leftrightarrow & -990x-330x& = & 22-60 \\\Leftrightarrow & \color{red}{-1320} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1320} & & \\\Leftrightarrow & x = \frac{19}{660} & & \\ & V = \left\{ \frac{19}{660} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{3})& = & -3x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{4}{3}& = & -3x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{12}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-12} & = & \color{red}{-27x} +4 \\\Leftrightarrow & 72x \color{red}{-12} \color{blue}{+12} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+12} \\\Leftrightarrow & 72x+27x& = & 4+12 \\\Leftrightarrow & \color{red}{99} x& = & 16 \\\Leftrightarrow & x = \frac{16}{99} & & \\ & V = \left\{ \frac{16}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 28x+\frac{21}{8}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{+21} & = & \color{red}{-72x} +28 \\\Leftrightarrow & 224x \color{red}{+21} \color{blue}{-21} \color{blue}{+72x} & = & \color{red}{-72x} +28 \color{blue}{+72x} \color{blue}{-21} \\\Leftrightarrow & 224x+72x& = & 28-21 \\\Leftrightarrow & \color{red}{296} x& = & 7 \\\Leftrightarrow & x = \frac{7}{296} & & \\ & V = \left\{ \frac{7}{296} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-12}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{-12x} +8 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{+12x} & = & \color{red}{-12x} +8 \color{blue}{+12x} \color{blue}{+20} \\\Leftrightarrow & 45x+12x& = & 8+20 \\\Leftrightarrow & \color{red}{57} x& = & 28 \\\Leftrightarrow & x = \frac{28}{57} & & \\ & V = \left\{ \frac{28}{57} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -16x+\frac{20}{7}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-1344}{ \color{blue}{84} }x+ \frac{240}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -1344x \color{red}{+240} & = & \color{red}{-588x} +49 \\\Leftrightarrow & -1344x \color{red}{+240} \color{blue}{-240} \color{blue}{+588x} & = & \color{red}{-588x} +49 \color{blue}{+588x} \color{blue}{-240} \\\Leftrightarrow & -1344x+588x& = & 49-240 \\\Leftrightarrow & \color{red}{-756} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-756} & & \\\Leftrightarrow & x = \frac{191}{756} & & \\ & V = \left\{ \frac{191}{756} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{2})& = & -8x+\frac{9}{2} \\\Leftrightarrow & 21x+\frac{35}{2}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{42}{ \color{blue}{2} }x+ \frac{35}{ \color{blue}{2} })& = & (\frac{-16}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 42x \color{red}{+35} & = & \color{red}{-16x} +9 \\\Leftrightarrow & 42x \color{red}{+35} \color{blue}{-35} \color{blue}{+16x} & = & \color{red}{-16x} +9 \color{blue}{+16x} \color{blue}{-35} \\\Leftrightarrow & 42x+16x& = & 9-35 \\\Leftrightarrow & \color{red}{58} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{58} & & \\\Leftrightarrow & x = \frac{-13}{29} & & \\ & V = \left\{ \frac{-13}{29} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -9x+\frac{7}{4} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -9x+\frac{7}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{14}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{-72x} +14 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{+72x} & = & \color{red}{-72x} +14 \color{blue}{+72x} \color{blue}{+21} \\\Leftrightarrow & 224x+72x& = & 14+21 \\\Leftrightarrow & \color{red}{296} x& = & 35 \\\Leftrightarrow & x = \frac{35}{296} & & \\ & V = \left\{ \frac{35}{296} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{3}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{-24} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 160x \color{red}{-24} \color{blue}{+24} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+24} \\\Leftrightarrow & 160x+70x& = & 15+24 \\\Leftrightarrow & \color{red}{230} x& = & 39 \\\Leftrightarrow & x = \frac{39}{230} & & \\ & V = \left\{ \frac{39}{230} \right\} & \\\end{align}\)
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