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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{+6} & = & \color{red}{-49x} +9 \\\Leftrightarrow & -42x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -42x+49x& = & 9-6 \\\Leftrightarrow & \color{red}{7} x& = & 3 \\\Leftrightarrow & x = \frac{3}{7} & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-66} & = & \color{red}{-539x} +56 \\\Leftrightarrow & -462x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -462x+539x& = & 56+66 \\\Leftrightarrow & \color{red}{77} x& = & 122 \\\Leftrightarrow & x = \frac{122}{77} & & \\ & V = \left\{ \frac{122}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & -9x+\frac{5}{2} \\\Leftrightarrow & -20x+\frac{15}{4}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-36}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{-36x} +10 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{+36x} & = & \color{red}{-36x} +10 \color{blue}{+36x} \color{blue}{-15} \\\Leftrightarrow & -80x+36x& = & 10-15 \\\Leftrightarrow & \color{red}{-44} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-44} & & \\\Leftrightarrow & x = \frac{5}{44} & & \\ & V = \left\{ \frac{5}{44} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{16}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{240}{ \color{blue}{20} }x+ \frac{64}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 240x \color{red}{+64} & = & \color{red}{100x} +45 \\\Leftrightarrow & 240x \color{red}{+64} \color{blue}{-64} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{-64} \\\Leftrightarrow & 240x-100x& = & 45-64 \\\Leftrightarrow & \color{red}{140} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{140} & & \\ & V = \left\{ \frac{-19}{140} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -6x-\frac{10}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-30} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -126x \color{red}{-30} \color{blue}{+30} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+30} \\\Leftrightarrow & -126x+147x& = & 14+30 \\\Leftrightarrow & \color{red}{21} x& = & 44 \\\Leftrightarrow & x = \frac{44}{21} & & \\ & V = \left\{ \frac{44}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{6})& = & 2x+\frac{2}{7} \\\Leftrightarrow & -28x+\frac{35}{6}& = & 2x+\frac{2}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1176}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{84}{ \color{blue}{42} }x+ \frac{12}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1176x \color{red}{+245} & = & \color{red}{84x} +12 \\\Leftrightarrow & -1176x \color{red}{+245} \color{blue}{-245} \color{blue}{-84x} & = & \color{red}{84x} +12 \color{blue}{-84x} \color{blue}{-245} \\\Leftrightarrow & -1176x-84x& = & 12-245 \\\Leftrightarrow & \color{red}{-1260} x& = & -233 \\\Leftrightarrow & x = \frac{-233}{-1260} & & \\\Leftrightarrow & x = \frac{233}{1260} & & \\ & V = \left\{ \frac{233}{1260} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{3})& = & 9x+\frac{9}{11} \\\Leftrightarrow & 10x+\frac{20}{3}& = & 9x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+220} & = & \color{red}{297x} +27 \\\Leftrightarrow & 330x \color{red}{+220} \color{blue}{-220} \color{blue}{-297x} & = & \color{red}{297x} +27 \color{blue}{-297x} \color{blue}{-220} \\\Leftrightarrow & 330x-297x& = & 27-220 \\\Leftrightarrow & \color{red}{33} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{33} & & \\ & V = \left\{ \frac{-193}{33} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 9x+\frac{7}{12} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 9x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{144}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{324}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 144x \color{red}{-32} & = & \color{red}{324x} +21 \\\Leftrightarrow & 144x \color{red}{-32} \color{blue}{+32} \color{blue}{-324x} & = & \color{red}{324x} +21 \color{blue}{-324x} \color{blue}{+32} \\\Leftrightarrow & 144x-324x& = & 21+32 \\\Leftrightarrow & \color{red}{-180} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-180} & & \\\Leftrightarrow & x = \frac{-53}{180} & & \\ & V = \left\{ \frac{-53}{180} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{7})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{8}{7}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-140}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -140x \color{red}{-8} & = & \color{red}{-49x} +8 \\\Leftrightarrow & -140x \color{red}{-8} \color{blue}{+8} \color{blue}{+49x} & = & \color{red}{-49x} +8 \color{blue}{+49x} \color{blue}{+8} \\\Leftrightarrow & -140x+49x& = & 8+8 \\\Leftrightarrow & \color{red}{-91} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-91} & & \\\Leftrightarrow & x = \frac{-16}{91} & & \\ & V = \left\{ \frac{-16}{91} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & -7x+\frac{9}{4} \\\Leftrightarrow & 15x-\frac{15}{11}& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x- \frac{60}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{-308x} +99 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{+308x} & = & \color{red}{-308x} +99 \color{blue}{+308x} \color{blue}{+60} \\\Leftrightarrow & 660x+308x& = & 99+60 \\\Leftrightarrow & \color{red}{968} x& = & 159 \\\Leftrightarrow & x = \frac{159}{968} & & \\ & V = \left\{ \frac{159}{968} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{-4} & = & \color{red}{-35x} +2 \\\Leftrightarrow & -30x \color{red}{-4} \color{blue}{+4} \color{blue}{+35x} & = & \color{red}{-35x} +2 \color{blue}{+35x} \color{blue}{+4} \\\Leftrightarrow & -30x+35x& = & 2+4 \\\Leftrightarrow & \color{red}{5} x& = & 6 \\\Leftrightarrow & x = \frac{6}{5} & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+108} & = & \color{red}{135x} +20 \\\Leftrightarrow & -360x \color{red}{+108} \color{blue}{-108} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{-108} \\\Leftrightarrow & -360x-135x& = & 20-108 \\\Leftrightarrow & \color{red}{-495} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-495} & & \\\Leftrightarrow & x = \frac{8}{45} & & \\ & V = \left\{ \frac{8}{45} \right\} & \\\end{align}\)
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