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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{16}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{-16} & = & \color{red}{15x} +4 \\\Leftrightarrow & -36x \color{red}{-16} \color{blue}{+16} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+16} \\\Leftrightarrow & -36x-15x& = & 4+16 \\\Leftrightarrow & \color{red}{-51} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-51} & & \\\Leftrightarrow & x = \frac{-20}{51} & & \\ & V = \left\{ \frac{-20}{51} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{5}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{+35} & = & \color{red}{-9x} +8 \\\Leftrightarrow & -105x \color{red}{+35} \color{blue}{-35} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{-35} \\\Leftrightarrow & -105x+9x& = & 8-35 \\\Leftrightarrow & \color{red}{-96} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-96} & & \\\Leftrightarrow & x = \frac{9}{32} & & \\ & V = \left\{ \frac{9}{32} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{25}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{75}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+75} & = & \color{red}{231x} +22 \\\Leftrightarrow & -330x \color{red}{+75} \color{blue}{-75} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-75} \\\Leftrightarrow & -330x-231x& = & 22-75 \\\Leftrightarrow & \color{red}{-561} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-561} & & \\\Leftrightarrow & x = \frac{53}{561} & & \\ & V = \left\{ \frac{53}{561} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{24}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{264}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+264} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 1848x \color{red}{+264} \color{blue}{-264} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-264} \\\Leftrightarrow & 1848x+539x& = & 42-264 \\\Leftrightarrow & \color{red}{2387} x& = & -222 \\\Leftrightarrow & x = \frac{-222}{2387} & & \\ & V = \left\{ \frac{-222}{2387} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{2}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{6}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-42} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 1155x \color{red}{-42} \color{blue}{+42} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{+42} \\\Leftrightarrow & 1155x+539x& = & 88+42 \\\Leftrightarrow & \color{red}{1694} x& = & 130 \\\Leftrightarrow & x = \frac{130}{1694} & & \\\Leftrightarrow & x = \frac{65}{847} & & \\ & V = \left\{ \frac{65}{847} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{-168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+128} & = & \color{red}{-168x} +49 \\\Leftrightarrow & -1120x \color{red}{+128} \color{blue}{-128} \color{blue}{+168x} & = & \color{red}{-168x} +49 \color{blue}{+168x} \color{blue}{-128} \\\Leftrightarrow & -1120x+168x& = & 49-128 \\\Leftrightarrow & \color{red}{-952} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-952} & & \\\Leftrightarrow & x = \frac{79}{952} & & \\ & V = \left\{ \frac{79}{952} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{105x} +56 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+90} \\\Leftrightarrow & 378x-105x& = & 56+90 \\\Leftrightarrow & \color{red}{273} x& = & 146 \\\Leftrightarrow & x = \frac{146}{273} & & \\ & V = \left\{ \frac{146}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{-49x} +3 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +3 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -70x+49x& = & 3+10 \\\Leftrightarrow & \color{red}{-21} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-21} & & \\\Leftrightarrow & x = \frac{-13}{21} & & \\ & V = \left\{ \frac{-13}{21} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{4})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{25}{4}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+175} & = & \color{red}{-56x} +32 \\\Leftrightarrow & 420x \color{red}{+175} \color{blue}{-175} \color{blue}{+56x} & = & \color{red}{-56x} +32 \color{blue}{+56x} \color{blue}{-175} \\\Leftrightarrow & 420x+56x& = & 32-175 \\\Leftrightarrow & \color{red}{476} x& = & -143 \\\Leftrightarrow & x = \frac{-143}{476} & & \\ & V = \left\{ \frac{-143}{476} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{-84} & = & \color{red}{-245x} +30 \\\Leftrightarrow & -560x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & -560x+245x& = & 30+84 \\\Leftrightarrow & \color{red}{-315} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-315} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{3})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-600}{ \color{blue}{30} }x+ \frac{200}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -600x \color{red}{+200} & = & \color{red}{90x} +27 \\\Leftrightarrow & -600x \color{red}{+200} \color{blue}{-200} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{-200} \\\Leftrightarrow & -600x-90x& = & 27-200 \\\Leftrightarrow & \color{red}{-690} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-690} & & \\\Leftrightarrow & x = \frac{173}{690} & & \\ & V = \left\{ \frac{173}{690} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{6}{7}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+12} & = & \color{red}{70x} +21 \\\Leftrightarrow & -168x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +21 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -168x-70x& = & 21-12 \\\Leftrightarrow & \color{red}{-238} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-238} & & \\\Leftrightarrow & x = \frac{-9}{238} & & \\ & V = \left\{ \frac{-9}{238} \right\} & \\\end{align}\)
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