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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{11})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{20}{11}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{99x} +44 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{-99x} & = & \color{red}{99x} +44 \color{blue}{-99x} \color{blue}{-60} \\\Leftrightarrow & -264x-99x& = & 44-60 \\\Leftrightarrow & \color{red}{-363} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-363} & & \\\Leftrightarrow & x = \frac{16}{363} & & \\ & V = \left\{ \frac{16}{363} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x- \frac{24}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{-24} & = & \color{red}{35x} +6 \\\Leftrightarrow & 90x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & 90x-35x& = & 6+24 \\\Leftrightarrow & \color{red}{55} x& = & 30 \\\Leftrightarrow & x = \frac{30}{55} & & \\\Leftrightarrow & x = \frac{6}{11} & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-252}{ \color{blue}{42} }x- \frac{36}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -252x \color{red}{-36} & = & \color{red}{294x} +35 \\\Leftrightarrow & -252x \color{red}{-36} \color{blue}{+36} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{+36} \\\Leftrightarrow & -252x-294x& = & 35+36 \\\Leftrightarrow & \color{red}{-546} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-546} & & \\\Leftrightarrow & x = \frac{-71}{546} & & \\ & V = \left\{ \frac{-71}{546} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{11})& = & -8x+\frac{5}{7} \\\Leftrightarrow & -15x-\frac{12}{11}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-84} & = & \color{red}{-616x} +55 \\\Leftrightarrow & -1155x \color{red}{-84} \color{blue}{+84} \color{blue}{+616x} & = & \color{red}{-616x} +55 \color{blue}{+616x} \color{blue}{+84} \\\Leftrightarrow & -1155x+616x& = & 55+84 \\\Leftrightarrow & \color{red}{-539} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-539} & & \\\Leftrightarrow & x = \frac{-139}{539} & & \\ & V = \left\{ \frac{-139}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{2}{5})& = & 5x+\frac{9}{5} \\\Leftrightarrow & 24x-\frac{12}{5}& = & 5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{25x} +9 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +9 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 120x-25x& = & 9+12 \\\Leftrightarrow & \color{red}{95} x& = & 21 \\\Leftrightarrow & x = \frac{21}{95} & & \\ & V = \left\{ \frac{21}{95} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-176} & = & \color{red}{-231x} +14 \\\Leftrightarrow & -1540x \color{red}{-176} \color{blue}{+176} \color{blue}{+231x} & = & \color{red}{-231x} +14 \color{blue}{+231x} \color{blue}{+176} \\\Leftrightarrow & -1540x+231x& = & 14+176 \\\Leftrightarrow & \color{red}{-1309} x& = & 190 \\\Leftrightarrow & x = \frac{190}{-1309} & & \\\Leftrightarrow & x = \frac{-190}{1309} & & \\ & V = \left\{ \frac{-190}{1309} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{2}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-80} & = & \color{red}{168x} +49 \\\Leftrightarrow & 1120x \color{red}{-80} \color{blue}{+80} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{+80} \\\Leftrightarrow & 1120x-168x& = & 49+80 \\\Leftrightarrow & \color{red}{952} x& = & 129 \\\Leftrightarrow & x = \frac{129}{952} & & \\ & V = \left\{ \frac{129}{952} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{5})& = & -3x+\frac{3}{11} \\\Leftrightarrow & 28x-\frac{28}{5}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-308} & = & \color{red}{-165x} +15 \\\Leftrightarrow & 1540x \color{red}{-308} \color{blue}{+308} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{+308} \\\Leftrightarrow & 1540x+165x& = & 15+308 \\\Leftrightarrow & \color{red}{1705} x& = & 323 \\\Leftrightarrow & x = \frac{323}{1705} & & \\ & V = \left\{ \frac{323}{1705} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{3})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{8}{3}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+56} & = & \color{red}{-105x} +6 \\\Leftrightarrow & -252x \color{red}{+56} \color{blue}{-56} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-56} \\\Leftrightarrow & -252x+105x& = & 6-56 \\\Leftrightarrow & \color{red}{-147} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-147} & & \\\Leftrightarrow & x = \frac{50}{147} & & \\ & V = \left\{ \frac{50}{147} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 15-84 \\\Leftrightarrow & \color{red}{-595} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-595} & & \\\Leftrightarrow & x = \frac{69}{595} & & \\ & V = \left\{ \frac{69}{595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-140} & = & \color{red}{441x} +90 \\\Leftrightarrow & 1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+140} \\\Leftrightarrow & 1260x-441x& = & 90+140 \\\Leftrightarrow & \color{red}{819} x& = & 230 \\\Leftrightarrow & x = \frac{230}{819} & & \\ & V = \left\{ \frac{230}{819} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{-30} \\\Leftrightarrow & 330x+275x& = & 66-30 \\\Leftrightarrow & \color{red}{605} x& = & 36 \\\Leftrightarrow & x = \frac{36}{605} & & \\ & V = \left\{ \frac{36}{605} \right\} & \\\end{align}\)
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