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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{2}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-54} & = & \color{red}{-441x} +35 \\\Leftrightarrow & 756x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & 756x+441x& = & 35+54 \\\Leftrightarrow & \color{red}{1197} x& = & 89 \\\Leftrightarrow & x = \frac{89}{1197} & & \\ & V = \left\{ \frac{89}{1197} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-180} & = & \color{red}{-315x} +70 \\\Leftrightarrow & 756x \color{red}{-180} \color{blue}{+180} \color{blue}{+315x} & = & \color{red}{-315x} +70 \color{blue}{+315x} \color{blue}{+180} \\\Leftrightarrow & 756x+315x& = & 70+180 \\\Leftrightarrow & \color{red}{1071} x& = & 250 \\\Leftrightarrow & x = \frac{250}{1071} & & \\ & V = \left\{ \frac{250}{1071} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{4})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{9}{4}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+45} & = & \color{red}{100x} +12 \\\Leftrightarrow & -240x \color{red}{+45} \color{blue}{-45} \color{blue}{-100x} & = & \color{red}{100x} +12 \color{blue}{-100x} \color{blue}{-45} \\\Leftrightarrow & -240x-100x& = & 12-45 \\\Leftrightarrow & \color{red}{-340} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-340} & & \\\Leftrightarrow & x = \frac{33}{340} & & \\ & V = \left\{ \frac{33}{340} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x-\frac{8}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & -24x+27x& = & 4+8 \\\Leftrightarrow & \color{red}{3} x& = & 12 \\\Leftrightarrow & x = \frac{12}{3} & & \\\Leftrightarrow & x = 4 & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1260}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1260x \color{red}{-300} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -1260x \color{red}{-300} \color{blue}{+300} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{+300} \\\Leftrightarrow & -1260x+490x& = & 49+300 \\\Leftrightarrow & \color{red}{-770} x& = & 349 \\\Leftrightarrow & x = \frac{349}{-770} & & \\\Leftrightarrow & x = \frac{-349}{770} & & \\ & V = \left\{ \frac{-349}{770} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -25x-\frac{20}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{-100} & = & \color{red}{315x} +42 \\\Leftrightarrow & -875x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & -875x-315x& = & 42+100 \\\Leftrightarrow & \color{red}{-1190} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-1190} & & \\\Leftrightarrow & x = \frac{-71}{595} & & \\ & V = \left\{ \frac{-71}{595} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x+ \frac{147}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{+147} & = & \color{red}{-385x} +55 \\\Leftrightarrow & 1078x \color{red}{+147} \color{blue}{-147} \color{blue}{+385x} & = & \color{red}{-385x} +55 \color{blue}{+385x} \color{blue}{-147} \\\Leftrightarrow & 1078x+385x& = & 55-147 \\\Leftrightarrow & \color{red}{1463} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{1463} & & \\ & V = \left\{ \frac{-92}{1463} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+126} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 924x \color{red}{+126} \color{blue}{-126} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-126} \\\Leftrightarrow & 924x+385x& = & 22-126 \\\Leftrightarrow & \color{red}{1309} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{1309} & & \\ & V = \left\{ \frac{-104}{1309} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{110x} +33 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-36} \\\Leftrightarrow & 396x-110x& = & 33-36 \\\Leftrightarrow & \color{red}{286} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{286} & & \\ & V = \left\{ \frac{-3}{286} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -30x+\frac{24}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{120}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+120} & = & \color{red}{385x} +66 \\\Leftrightarrow & -1650x \color{red}{+120} \color{blue}{-120} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-120} \\\Leftrightarrow & -1650x-385x& = & 66-120 \\\Leftrightarrow & \color{red}{-2035} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-2035} & & \\\Leftrightarrow & x = \frac{54}{2035} & & \\ & V = \left\{ \frac{54}{2035} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -5x+\frac{7}{8} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{432}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-360}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 432x \color{red}{+64} & = & \color{red}{-360x} +63 \\\Leftrightarrow & 432x \color{red}{+64} \color{blue}{-64} \color{blue}{+360x} & = & \color{red}{-360x} +63 \color{blue}{+360x} \color{blue}{-64} \\\Leftrightarrow & 432x+360x& = & 63-64 \\\Leftrightarrow & \color{red}{792} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{792} & & \\ & V = \left\{ \frac{-1}{792} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -9x+\frac{12}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-594}{ \color{blue}{66} }x+ \frac{72}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -594x \color{red}{+72} & = & \color{red}{-330x} +55 \\\Leftrightarrow & -594x \color{red}{+72} \color{blue}{-72} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-72} \\\Leftrightarrow & -594x+330x& = & 55-72 \\\Leftrightarrow & \color{red}{-264} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-264} & & \\\Leftrightarrow & x = \frac{17}{264} & & \\ & V = \left\{ \frac{17}{264} \right\} & \\\end{align}\)
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