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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{-385x} +63 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{+385x} & = & \color{red}{-385x} +63 \color{blue}{+385x} \color{blue}{+110} \\\Leftrightarrow & -308x+385x& = & 63+110 \\\Leftrightarrow & \color{red}{77} x& = & 173 \\\Leftrightarrow & x = \frac{173}{77} & & \\ & V = \left\{ \frac{173}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{4})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 4 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{60x} +5 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +5 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & -144x-60x& = & 5+45 \\\Leftrightarrow & \color{red}{-204} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-204} & & \\\Leftrightarrow & x = \frac{-25}{102} & & \\ & V = \left\{ \frac{-25}{102} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{+21} & = & \color{red}{56x} +18 \\\Leftrightarrow & -224x \color{red}{+21} \color{blue}{-21} \color{blue}{-56x} & = & \color{red}{56x} +18 \color{blue}{-56x} \color{blue}{-21} \\\Leftrightarrow & -224x-56x& = & 18-21 \\\Leftrightarrow & \color{red}{-280} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-280} & & \\\Leftrightarrow & x = \frac{3}{280} & & \\ & V = \left\{ \frac{3}{280} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+108} & = & \color{red}{-225x} +10 \\\Leftrightarrow & -405x \color{red}{+108} \color{blue}{-108} \color{blue}{+225x} & = & \color{red}{-225x} +10 \color{blue}{+225x} \color{blue}{-108} \\\Leftrightarrow & -405x+225x& = & 10-108 \\\Leftrightarrow & \color{red}{-180} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-180} & & \\\Leftrightarrow & x = \frac{49}{90} & & \\ & V = \left\{ \frac{49}{90} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{9})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{20}{9}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+220} & = & \color{red}{-495x} +45 \\\Leftrightarrow & -1188x \color{red}{+220} \color{blue}{-220} \color{blue}{+495x} & = & \color{red}{-495x} +45 \color{blue}{+495x} \color{blue}{-220} \\\Leftrightarrow & -1188x+495x& = & 45-220 \\\Leftrightarrow & \color{red}{-693} x& = & -175 \\\Leftrightarrow & x = \frac{-175}{-693} & & \\\Leftrightarrow & x = \frac{25}{99} & & \\ & V = \left\{ \frac{25}{99} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{12}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{25x} +6 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -120x-25x& = & 6+12 \\\Leftrightarrow & \color{red}{-145} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-145} & & \\\Leftrightarrow & x = \frac{-18}{145} & & \\ & V = \left\{ \frac{-18}{145} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{5}{2})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 9x-\frac{15}{2}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{162}{ \color{blue}{18} }x- \frac{135}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 162x \color{red}{-135} & = & \color{red}{-126x} +8 \\\Leftrightarrow & 162x \color{red}{-135} \color{blue}{+135} \color{blue}{+126x} & = & \color{red}{-126x} +8 \color{blue}{+126x} \color{blue}{+135} \\\Leftrightarrow & 162x+126x& = & 8+135 \\\Leftrightarrow & \color{red}{288} x& = & 143 \\\Leftrightarrow & x = \frac{143}{288} & & \\ & V = \left\{ \frac{143}{288} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{4})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{25}{4}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{125}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+125} & = & \color{red}{60x} +18 \\\Leftrightarrow & 400x \color{red}{+125} \color{blue}{-125} \color{blue}{-60x} & = & \color{red}{60x} +18 \color{blue}{-60x} \color{blue}{-125} \\\Leftrightarrow & 400x-60x& = & 18-125 \\\Leftrightarrow & \color{red}{340} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{340} & & \\ & V = \left\{ \frac{-107}{340} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 3x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-90} & = & \color{red}{189x} +14 \\\Leftrightarrow & -1260x \color{red}{-90} \color{blue}{+90} \color{blue}{-189x} & = & \color{red}{189x} +14 \color{blue}{-189x} \color{blue}{+90} \\\Leftrightarrow & -1260x-189x& = & 14+90 \\\Leftrightarrow & \color{red}{-1449} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-1449} & & \\\Leftrightarrow & x = \frac{-104}{1449} & & \\ & V = \left\{ \frac{-104}{1449} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{135x} +20 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{-12} \\\Leftrightarrow & -120x-135x& = & 20-12 \\\Leftrightarrow & \color{red}{-255} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-255} & & \\\Leftrightarrow & x = \frac{-8}{255} & & \\ & V = \left\{ \frac{-8}{255} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{7})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 18x+\frac{18}{7}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{756}{ \color{blue}{42} }x+ \frac{108}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 756x \color{red}{+108} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 756x \color{red}{+108} \color{blue}{-108} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-108} \\\Leftrightarrow & 756x+210x& = & 35-108 \\\Leftrightarrow & \color{red}{966} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{966} & & \\ & V = \left\{ \frac{-73}{966} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & -3x+\frac{4}{7} \\\Leftrightarrow & -14x-\frac{21}{8}& = & -3x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{-147} & = & \color{red}{-168x} +32 \\\Leftrightarrow & -784x \color{red}{-147} \color{blue}{+147} \color{blue}{+168x} & = & \color{red}{-168x} +32 \color{blue}{+168x} \color{blue}{+147} \\\Leftrightarrow & -784x+168x& = & 32+147 \\\Leftrightarrow & \color{red}{-616} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-616} & & \\\Leftrightarrow & x = \frac{-179}{616} & & \\ & V = \left\{ \frac{-179}{616} \right\} & \\\end{align}\)
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