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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{2}{7})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -20x+\frac{10}{7}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1400}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1400x \color{red}{+100} & = & \color{red}{-630x} +21 \\\Leftrightarrow & -1400x \color{red}{+100} \color{blue}{-100} \color{blue}{+630x} & = & \color{red}{-630x} +21 \color{blue}{+630x} \color{blue}{-100} \\\Leftrightarrow & -1400x+630x& = & 21-100 \\\Leftrightarrow & \color{red}{-770} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-770} & & \\\Leftrightarrow & x = \frac{79}{770} & & \\ & V = \left\{ \frac{79}{770} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{2}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -9x+\frac{6}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{+54} & = & \color{red}{-315x} +28 \\\Leftrightarrow & -567x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & -567x+315x& = & 28-54 \\\Leftrightarrow & \color{red}{-252} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-252} & & \\\Leftrightarrow & x = \frac{13}{126} & & \\ & V = \left\{ \frac{13}{126} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+220} & = & \color{red}{-231x} +35 \\\Leftrightarrow & -616x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +35 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & -616x+231x& = & 35-220 \\\Leftrightarrow & \color{red}{-385} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{-385} & & \\\Leftrightarrow & x = \frac{37}{77} & & \\ & V = \left\{ \frac{37}{77} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -10x+\frac{4}{5}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+44} & = & \color{red}{385x} +45 \\\Leftrightarrow & -550x \color{red}{+44} \color{blue}{-44} \color{blue}{-385x} & = & \color{red}{385x} +45 \color{blue}{-385x} \color{blue}{-44} \\\Leftrightarrow & -550x-385x& = & 45-44 \\\Leftrightarrow & \color{red}{-935} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-935} & & \\\Leftrightarrow & x = \frac{-1}{935} & & \\ & V = \left\{ \frac{-1}{935} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+90} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 990x \color{red}{+90} \color{blue}{-90} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-90} \\\Leftrightarrow & 990x+275x& = & 66-90 \\\Leftrightarrow & \color{red}{1265} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{1265} & & \\ & V = \left\{ \frac{-24}{1265} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{48}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{48x} +16 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{-48x} & = & \color{red}{48x} +16 \color{blue}{-48x} \color{blue}{-45} \\\Leftrightarrow & 180x-48x& = & 16-45 \\\Leftrightarrow & \color{red}{132} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{132} & & \\ & V = \left\{ \frac{-29}{132} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-42}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -42x \color{red}{-6} & = & \color{red}{49x} +10 \\\Leftrightarrow & -42x \color{red}{-6} \color{blue}{+6} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{+6} \\\Leftrightarrow & -42x-49x& = & 10+6 \\\Leftrightarrow & \color{red}{-91} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-91} & & \\\Leftrightarrow & x = \frac{-16}{91} & & \\ & V = \left\{ \frac{-16}{91} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{5})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 8x-\frac{8}{5}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-88} & = & \color{red}{165x} +15 \\\Leftrightarrow & 440x \color{red}{-88} \color{blue}{+88} \color{blue}{-165x} & = & \color{red}{165x} +15 \color{blue}{-165x} \color{blue}{+88} \\\Leftrightarrow & 440x-165x& = & 15+88 \\\Leftrightarrow & \color{red}{275} x& = & 103 \\\Leftrightarrow & x = \frac{103}{275} & & \\ & V = \left\{ \frac{103}{275} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-840}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -840x \color{red}{+120} & = & \color{red}{196x} +35 \\\Leftrightarrow & -840x \color{red}{+120} \color{blue}{-120} \color{blue}{-196x} & = & \color{red}{196x} +35 \color{blue}{-196x} \color{blue}{-120} \\\Leftrightarrow & -840x-196x& = & 35-120 \\\Leftrightarrow & \color{red}{-1036} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-1036} & & \\\Leftrightarrow & x = \frac{85}{1036} & & \\ & V = \left\{ \frac{85}{1036} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{600}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 600x \color{red}{+96} & = & \color{red}{140x} +35 \\\Leftrightarrow & 600x \color{red}{+96} \color{blue}{-96} \color{blue}{-140x} & = & \color{red}{140x} +35 \color{blue}{-140x} \color{blue}{-96} \\\Leftrightarrow & 600x-140x& = & 35-96 \\\Leftrightarrow & \color{red}{460} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{460} & & \\ & V = \left\{ \frac{-61}{460} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{6})& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-\frac{35}{6}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{-35} & = & \color{red}{-48x} +16 \\\Leftrightarrow & -126x \color{red}{-35} \color{blue}{+35} \color{blue}{+48x} & = & \color{red}{-48x} +16 \color{blue}{+48x} \color{blue}{+35} \\\Leftrightarrow & -126x+48x& = & 16+35 \\\Leftrightarrow & \color{red}{-78} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-78} & & \\\Leftrightarrow & x = \frac{-17}{26} & & \\ & V = \left\{ \frac{-17}{26} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{100}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-100} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -120x \color{red}{-100} \color{blue}{+100} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{+100} \\\Leftrightarrow & -120x+135x& = & 18+100 \\\Leftrightarrow & \color{red}{15} x& = & 118 \\\Leftrightarrow & x = \frac{118}{15} & & \\ & V = \left\{ \frac{118}{15} \right\} & \\\end{align}\)
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