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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{11})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{35}{11}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2310}{ \color{blue}{110} }x+ \frac{350}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2310x \color{red}{+350} & = & \color{red}{-880x} +99 \\\Leftrightarrow & -2310x \color{red}{+350} \color{blue}{-350} \color{blue}{+880x} & = & \color{red}{-880x} +99 \color{blue}{+880x} \color{blue}{-350} \\\Leftrightarrow & -2310x+880x& = & 99-350 \\\Leftrightarrow & \color{red}{-1430} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{-1430} & & \\\Leftrightarrow & x = \frac{251}{1430} & & \\ & V = \left\{ \frac{251}{1430} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{4})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+105} & = & \color{red}{196x} +16 \\\Leftrightarrow & 420x \color{red}{+105} \color{blue}{-105} \color{blue}{-196x} & = & \color{red}{196x} +16 \color{blue}{-196x} \color{blue}{-105} \\\Leftrightarrow & 420x-196x& = & 16-105 \\\Leftrightarrow & \color{red}{224} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{224} & & \\ & V = \left\{ \frac{-89}{224} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{11})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -21x+\frac{21}{11}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x+ \frac{42}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{+42} & = & \color{red}{176x} +99 \\\Leftrightarrow & -462x \color{red}{+42} \color{blue}{-42} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{-42} \\\Leftrightarrow & -462x-176x& = & 99-42 \\\Leftrightarrow & \color{red}{-638} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-638} & & \\\Leftrightarrow & x = \frac{-57}{638} & & \\ & V = \left\{ \frac{-57}{638} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-36} & = & \color{red}{154x} +77 \\\Leftrightarrow & 660x \color{red}{-36} \color{blue}{+36} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{+36} \\\Leftrightarrow & 660x-154x& = & 77+36 \\\Leftrightarrow & \color{red}{506} x& = & 113 \\\Leftrightarrow & x = \frac{113}{506} & & \\ & V = \left\{ \frac{113}{506} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{2})& = & -6x+\frac{3}{10} \\\Leftrightarrow & -25x-\frac{15}{2}& = & -6x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-60}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{-75} & = & \color{red}{-60x} +3 \\\Leftrightarrow & -250x \color{red}{-75} \color{blue}{+75} \color{blue}{+60x} & = & \color{red}{-60x} +3 \color{blue}{+60x} \color{blue}{+75} \\\Leftrightarrow & -250x+60x& = & 3+75 \\\Leftrightarrow & \color{red}{-190} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-190} & & \\\Leftrightarrow & x = \frac{-39}{95} & & \\ & V = \left\{ \frac{-39}{95} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-154} & = & \color{red}{-99x} +18 \\\Leftrightarrow & 462x \color{red}{-154} \color{blue}{+154} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{+154} \\\Leftrightarrow & 462x+99x& = & 18+154 \\\Leftrightarrow & \color{red}{561} x& = & 172 \\\Leftrightarrow & x = \frac{172}{561} & & \\ & V = \left\{ \frac{172}{561} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -14x-\frac{35}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1008}{ \color{blue}{72} }x- \frac{280}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1008x \color{red}{-280} & = & \color{red}{-216x} +63 \\\Leftrightarrow & -1008x \color{red}{-280} \color{blue}{+280} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{+280} \\\Leftrightarrow & -1008x+216x& = & 63+280 \\\Leftrightarrow & \color{red}{-792} x& = & 343 \\\Leftrightarrow & x = \frac{343}{-792} & & \\\Leftrightarrow & x = \frac{-343}{792} & & \\ & V = \left\{ \frac{-343}{792} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 8x+\frac{5}{8} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 8x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{200}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 200x \color{red}{-30} & = & \color{red}{64x} +5 \\\Leftrightarrow & 200x \color{red}{-30} \color{blue}{+30} \color{blue}{-64x} & = & \color{red}{64x} +5 \color{blue}{-64x} \color{blue}{+30} \\\Leftrightarrow & 200x-64x& = & 5+30 \\\Leftrightarrow & \color{red}{136} x& = & 35 \\\Leftrightarrow & x = \frac{35}{136} & & \\ & V = \left\{ \frac{35}{136} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{9})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{189x} +36 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{-189x} & = & \color{red}{189x} +36 \color{blue}{-189x} \color{blue}{-28} \\\Leftrightarrow & 252x-189x& = & 36-28 \\\Leftrightarrow & \color{red}{63} x& = & 8 \\\Leftrightarrow & x = \frac{8}{63} & & \\ & V = \left\{ \frac{8}{63} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & -330x+385x& = & 66+30 \\\Leftrightarrow & \color{red}{55} x& = & 96 \\\Leftrightarrow & x = \frac{96}{55} & & \\ & V = \left\{ \frac{96}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & -2x+\frac{10}{7} \\\Leftrightarrow & 9x-\frac{6}{7}& = & -2x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{-6} & = & \color{red}{-14x} +10 \\\Leftrightarrow & 63x \color{red}{-6} \color{blue}{+6} \color{blue}{+14x} & = & \color{red}{-14x} +10 \color{blue}{+14x} \color{blue}{+6} \\\Leftrightarrow & 63x+14x& = & 10+6 \\\Leftrightarrow & \color{red}{77} x& = & 16 \\\Leftrightarrow & x = \frac{16}{77} & & \\ & V = \left\{ \frac{16}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{8}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-440}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{165x} +66 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{+40} \\\Leftrightarrow & -440x-165x& = & 66+40 \\\Leftrightarrow & \color{red}{-605} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-605} & & \\\Leftrightarrow & x = \frac{-106}{605} & & \\ & V = \left\{ \frac{-106}{605} \right\} & \\\end{align}\)
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