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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{8}{9}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{-315x} +81 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +81 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & 252x+315x& = & 81-56 \\\Leftrightarrow & \color{red}{567} x& = & 25 \\\Leftrightarrow & x = \frac{25}{567} & & \\ & V = \left\{ \frac{25}{567} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{5})& = & -9x+\frac{5}{8} \\\Leftrightarrow & -8x-\frac{16}{5}& = & -9x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x- \frac{128}{ \color{blue}{40} })& = & (\frac{-360}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{-128} & = & \color{red}{-360x} +25 \\\Leftrightarrow & -320x \color{red}{-128} \color{blue}{+128} \color{blue}{+360x} & = & \color{red}{-360x} +25 \color{blue}{+360x} \color{blue}{+128} \\\Leftrightarrow & -320x+360x& = & 25+128 \\\Leftrightarrow & \color{red}{40} x& = & 153 \\\Leftrightarrow & x = \frac{153}{40} & & \\ & V = \left\{ \frac{153}{40} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-84} & = & \color{red}{245x} +40 \\\Leftrightarrow & 280x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 280x-245x& = & 40+84 \\\Leftrightarrow & \color{red}{35} x& = & 124 \\\Leftrightarrow & x = \frac{124}{35} & & \\ & V = \left\{ \frac{124}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+32} & = & \color{red}{70x} +21 \\\Leftrightarrow & -168x \color{red}{+32} \color{blue}{-32} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-32} \\\Leftrightarrow & -168x-70x& = & 21-32 \\\Leftrightarrow & \color{red}{-238} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-238} & & \\\Leftrightarrow & x = \frac{11}{238} & & \\ & V = \left\{ \frac{11}{238} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{3})& = & -9x+\frac{2}{7} \\\Leftrightarrow & -4x-\frac{8}{3}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-56} & = & \color{red}{-189x} +6 \\\Leftrightarrow & -84x \color{red}{-56} \color{blue}{+56} \color{blue}{+189x} & = & \color{red}{-189x} +6 \color{blue}{+189x} \color{blue}{+56} \\\Leftrightarrow & -84x+189x& = & 6+56 \\\Leftrightarrow & \color{red}{105} x& = & 62 \\\Leftrightarrow & x = \frac{62}{105} & & \\ & V = \left\{ \frac{62}{105} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & -7x+\frac{7}{3} \\\Leftrightarrow & 25x+\frac{15}{11}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+45} & = & \color{red}{-231x} +77 \\\Leftrightarrow & 825x \color{red}{+45} \color{blue}{-45} \color{blue}{+231x} & = & \color{red}{-231x} +77 \color{blue}{+231x} \color{blue}{-45} \\\Leftrightarrow & 825x+231x& = & 77-45 \\\Leftrightarrow & \color{red}{1056} x& = & 32 \\\Leftrightarrow & x = \frac{32}{1056} & & \\\Leftrightarrow & x = \frac{1}{33} & & \\ & V = \left\{ \frac{1}{33} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{16}{3}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-112} & = & \color{red}{-147x} +27 \\\Leftrightarrow & -420x \color{red}{-112} \color{blue}{+112} \color{blue}{+147x} & = & \color{red}{-147x} +27 \color{blue}{+147x} \color{blue}{+112} \\\Leftrightarrow & -420x+147x& = & 27+112 \\\Leftrightarrow & \color{red}{-273} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-273} & & \\\Leftrightarrow & x = \frac{-139}{273} & & \\ & V = \left\{ \frac{-139}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{7})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+6} & = & \color{red}{-35x} +5 \\\Leftrightarrow & -84x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +5 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & -84x+35x& = & 5-6 \\\Leftrightarrow & \color{red}{-49} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-49} & & \\\Leftrightarrow & x = \frac{1}{49} & & \\ & V = \left\{ \frac{1}{49} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -350x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{-105} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-105} & & \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{18}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{120}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+18} \\\Leftrightarrow & 120x+25x& = & 6+18 \\\Leftrightarrow & \color{red}{145} x& = & 24 \\\Leftrightarrow & x = \frac{24}{145} & & \\ & V = \left\{ \frac{24}{145} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{11})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 14x+\frac{35}{11}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1232}{ \color{blue}{88} }x+ \frac{280}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1232x \color{red}{+280} & = & \color{red}{440x} +33 \\\Leftrightarrow & 1232x \color{red}{+280} \color{blue}{-280} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{-280} \\\Leftrightarrow & 1232x-440x& = & 33-280 \\\Leftrightarrow & \color{red}{792} x& = & -247 \\\Leftrightarrow & x = \frac{-247}{792} & & \\ & V = \left\{ \frac{-247}{792} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{-231x} +14 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{+231x} & = & \color{red}{-231x} +14 \color{blue}{+231x} \color{blue}{-66} \\\Leftrightarrow & 616x+231x& = & 14-66 \\\Leftrightarrow & \color{red}{847} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{847} & & \\ & V = \left\{ \frac{-52}{847} \right\} & \\\end{align}\)
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