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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-176} & = & \color{red}{385x} +70 \\\Leftrightarrow & 924x \color{red}{-176} \color{blue}{+176} \color{blue}{-385x} & = & \color{red}{385x} +70 \color{blue}{-385x} \color{blue}{+176} \\\Leftrightarrow & 924x-385x& = & 70+176 \\\Leftrightarrow & \color{red}{539} x& = & 246 \\\Leftrightarrow & x = \frac{246}{539} & & \\ & V = \left\{ \frac{246}{539} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{7})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{12}{7}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-336}{ \color{blue}{28} }x- \frac{48}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{-140x} +21 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +21 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -336x+140x& = & 21+48 \\\Leftrightarrow & \color{red}{-196} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-196} & & \\\Leftrightarrow & x = \frac{-69}{196} & & \\ & V = \left\{ \frac{-69}{196} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -5x+\frac{8}{5} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{-75x} +24 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{+75x} & = & \color{red}{-75x} +24 \color{blue}{+75x} \color{blue}{-70} \\\Leftrightarrow & -210x+75x& = & 24-70 \\\Leftrightarrow & \color{red}{-135} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-135} & & \\\Leftrightarrow & x = \frac{46}{135} & & \\ & V = \left\{ \frac{46}{135} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{3})& = & -8x+\frac{5}{7} \\\Leftrightarrow & 15x+\frac{25}{3}& = & -8x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x+ \frac{175}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{+175} & = & \color{red}{-168x} +15 \\\Leftrightarrow & 315x \color{red}{+175} \color{blue}{-175} \color{blue}{+168x} & = & \color{red}{-168x} +15 \color{blue}{+168x} \color{blue}{-175} \\\Leftrightarrow & 315x+168x& = & 15-175 \\\Leftrightarrow & \color{red}{483} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{483} & & \\ & V = \left\{ \frac{-160}{483} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{8})& = & -9x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{25}{8}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x- \frac{175}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{-175} & = & \color{red}{-504x} +48 \\\Leftrightarrow & 1120x \color{red}{-175} \color{blue}{+175} \color{blue}{+504x} & = & \color{red}{-504x} +48 \color{blue}{+504x} \color{blue}{+175} \\\Leftrightarrow & 1120x+504x& = & 48+175 \\\Leftrightarrow & \color{red}{1624} x& = & 223 \\\Leftrightarrow & x = \frac{223}{1624} & & \\ & V = \left\{ \frac{223}{1624} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 18x-\frac{30}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x- \frac{240}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{-240} & = & \color{red}{440x} +77 \\\Leftrightarrow & 1584x \color{red}{-240} \color{blue}{+240} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{+240} \\\Leftrightarrow & 1584x-440x& = & 77+240 \\\Leftrightarrow & \color{red}{1144} x& = & 317 \\\Leftrightarrow & x = \frac{317}{1144} & & \\ & V = \left\{ \frac{317}{1144} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x+\frac{8}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+56} & = & \color{red}{147x} +30 \\\Leftrightarrow & -126x \color{red}{+56} \color{blue}{-56} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{-56} \\\Leftrightarrow & -126x-147x& = & 30-56 \\\Leftrightarrow & \color{red}{-273} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-273} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-14} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -42x \color{red}{-14} \color{blue}{+14} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{+14} \\\Leftrightarrow & -42x+9x& = & 4+14 \\\Leftrightarrow & \color{red}{-33} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-33} & & \\\Leftrightarrow & x = \frac{-6}{11} & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & 3x+\frac{6}{5} \\\Leftrightarrow & -20x-\frac{10}{3}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{50}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-50} & = & \color{red}{45x} +18 \\\Leftrightarrow & -300x \color{red}{-50} \color{blue}{+50} \color{blue}{-45x} & = & \color{red}{45x} +18 \color{blue}{-45x} \color{blue}{+50} \\\Leftrightarrow & -300x-45x& = & 18+50 \\\Leftrightarrow & \color{red}{-345} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-345} & & \\\Leftrightarrow & x = \frac{-68}{345} & & \\ & V = \left\{ \frac{-68}{345} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & 9x+\frac{5}{4} \\\Leftrightarrow & -8x+\frac{6}{7}& = & 9x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{+24} & = & \color{red}{252x} +35 \\\Leftrightarrow & -224x \color{red}{+24} \color{blue}{-24} \color{blue}{-252x} & = & \color{red}{252x} +35 \color{blue}{-252x} \color{blue}{-24} \\\Leftrightarrow & -224x-252x& = & 35-24 \\\Leftrightarrow & \color{red}{-476} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-476} & & \\\Leftrightarrow & x = \frac{-11}{476} & & \\ & V = \left\{ \frac{-11}{476} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & 7x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{70x} +9 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +9 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 120x-70x& = & 9+24 \\\Leftrightarrow & \color{red}{50} x& = & 33 \\\Leftrightarrow & x = \frac{33}{50} & & \\ & V = \left\{ \frac{33}{50} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{-77x} +4 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{-18} \\\Leftrightarrow & -330x+77x& = & 4-18 \\\Leftrightarrow & \color{red}{-253} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-253} & & \\\Leftrightarrow & x = \frac{14}{253} & & \\ & V = \left\{ \frac{14}{253} \right\} & \\\end{align}\)
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