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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{64}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+64} & = & \color{red}{-84x} +21 \\\Leftrightarrow & -560x \color{red}{+64} \color{blue}{-64} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{-64} \\\Leftrightarrow & -560x+84x& = & 21-64 \\\Leftrightarrow & \color{red}{-476} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-476} & & \\\Leftrightarrow & x = \frac{43}{476} & & \\ & V = \left\{ \frac{43}{476} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{3}{10})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-810}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{100}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -810x \color{red}{-81} & = & \color{red}{450x} +100 \\\Leftrightarrow & -810x \color{red}{-81} \color{blue}{+81} \color{blue}{-450x} & = & \color{red}{450x} +100 \color{blue}{-450x} \color{blue}{+81} \\\Leftrightarrow & -810x-450x& = & 100+81 \\\Leftrightarrow & \color{red}{-1260} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1260} & & \\\Leftrightarrow & x = \frac{-181}{1260} & & \\ & V = \left\{ \frac{-181}{1260} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 180x+75x& = & 20+36 \\\Leftrightarrow & \color{red}{255} x& = & 56 \\\Leftrightarrow & x = \frac{56}{255} & & \\ & V = \left\{ \frac{56}{255} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -21x+\frac{14}{3}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -441x \color{red}{+98} & = & \color{red}{-168x} +12 \\\Leftrightarrow & -441x \color{red}{+98} \color{blue}{-98} \color{blue}{+168x} & = & \color{red}{-168x} +12 \color{blue}{+168x} \color{blue}{-98} \\\Leftrightarrow & -441x+168x& = & 12-98 \\\Leftrightarrow & \color{red}{-273} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-273} & & \\\Leftrightarrow & x = \frac{86}{273} & & \\ & V = \left\{ \frac{86}{273} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{15}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{75}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-75} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-75} \color{blue}{+75} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+75} \\\Leftrightarrow & 420x-175x& = & 42+75 \\\Leftrightarrow & \color{red}{245} x& = & 117 \\\Leftrightarrow & x = \frac{117}{245} & & \\ & V = \left\{ \frac{117}{245} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{5})& = & -6x+\frac{4}{5} \\\Leftrightarrow & 35x-\frac{28}{5}& = & -6x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{175}{ \color{blue}{5} }x- \frac{28}{ \color{blue}{5} })& = & (\frac{-30}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 175x \color{red}{-28} & = & \color{red}{-30x} +4 \\\Leftrightarrow & 175x \color{red}{-28} \color{blue}{+28} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{+28} \\\Leftrightarrow & 175x+30x& = & 4+28 \\\Leftrightarrow & \color{red}{205} x& = & 32 \\\Leftrightarrow & x = \frac{32}{205} & & \\ & V = \left\{ \frac{32}{205} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-20} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -140x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & -140x+98x& = & 35+20 \\\Leftrightarrow & \color{red}{-42} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-42} & & \\\Leftrightarrow & x = \frac{-55}{42} & & \\ & V = \left\{ \frac{-55}{42} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{-8} & = & \color{red}{50x} +25 \\\Leftrightarrow & -40x \color{red}{-8} \color{blue}{+8} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{+8} \\\Leftrightarrow & -40x-50x& = & 25+8 \\\Leftrightarrow & \color{red}{-90} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-90} & & \\\Leftrightarrow & x = \frac{-11}{30} & & \\ & V = \left\{ \frac{-11}{30} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & -3x+\frac{8}{7} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-735}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -735x \color{red}{+245} & = & \color{red}{-63x} +24 \\\Leftrightarrow & -735x \color{red}{+245} \color{blue}{-245} \color{blue}{+63x} & = & \color{red}{-63x} +24 \color{blue}{+63x} \color{blue}{-245} \\\Leftrightarrow & -735x+63x& = & 24-245 \\\Leftrightarrow & \color{red}{-672} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-672} & & \\\Leftrightarrow & x = \frac{221}{672} & & \\ & V = \left\{ \frac{221}{672} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{4}{5})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -24x-\frac{24}{5}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{-25x} +2 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{+25x} & = & \color{red}{-25x} +2 \color{blue}{+25x} \color{blue}{+24} \\\Leftrightarrow & -120x+25x& = & 2+24 \\\Leftrightarrow & \color{red}{-95} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-95} & & \\\Leftrightarrow & x = \frac{-26}{95} & & \\ & V = \left\{ \frac{-26}{95} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{9})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+8} & = & \color{red}{-63x} +2 \\\Leftrightarrow & -144x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +2 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -144x+63x& = & 2-8 \\\Leftrightarrow & \color{red}{-81} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-81} & & \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-132} & = & \color{red}{275x} +10 \\\Leftrightarrow & -495x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -495x-275x& = & 10+132 \\\Leftrightarrow & \color{red}{-770} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-770} & & \\\Leftrightarrow & x = \frac{-71}{385} & & \\ & V = \left\{ \frac{-71}{385} \right\} & \\\end{align}\)
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