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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{+132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & -495x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -495x+385x& = & 50-132 \\\Leftrightarrow & \color{red}{-110} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-110} & & \\\Leftrightarrow & x = \frac{41}{55} & & \\ & V = \left\{ \frac{41}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{3}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & 6x+\frac{6}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{504}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 504x \color{red}{+72} & = & \color{red}{420x} +49 \\\Leftrightarrow & 504x \color{red}{+72} \color{blue}{-72} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{-72} \\\Leftrightarrow & 504x-420x& = & 49-72 \\\Leftrightarrow & \color{red}{84} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{84} & & \\ & V = \left\{ \frac{-23}{84} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{2})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -20x+\frac{25}{2}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x+ \frac{50}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{+50} & = & \color{red}{-28x} +7 \\\Leftrightarrow & -80x \color{red}{+50} \color{blue}{-50} \color{blue}{+28x} & = & \color{red}{-28x} +7 \color{blue}{+28x} \color{blue}{-50} \\\Leftrightarrow & -80x+28x& = & 7-50 \\\Leftrightarrow & \color{red}{-52} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-52} & & \\\Leftrightarrow & x = \frac{43}{52} & & \\ & V = \left\{ \frac{43}{52} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-84} & = & \color{red}{-175x} +15 \\\Leftrightarrow & -840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +15 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -840x+175x& = & 15+84 \\\Leftrightarrow & \color{red}{-665} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-665} & & \\\Leftrightarrow & x = \frac{-99}{665} & & \\ & V = \left\{ \frac{-99}{665} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{11})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -20x+\frac{20}{11}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+60} & = & \color{red}{-297x} +88 \\\Leftrightarrow & -660x \color{red}{+60} \color{blue}{-60} \color{blue}{+297x} & = & \color{red}{-297x} +88 \color{blue}{+297x} \color{blue}{-60} \\\Leftrightarrow & -660x+297x& = & 88-60 \\\Leftrightarrow & \color{red}{-363} x& = & 28 \\\Leftrightarrow & x = \frac{28}{-363} & & \\\Leftrightarrow & x = \frac{-28}{363} & & \\ & V = \left\{ \frac{-28}{363} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-168} & = & \color{red}{175x} +20 \\\Leftrightarrow & 630x \color{red}{-168} \color{blue}{+168} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+168} \\\Leftrightarrow & 630x-175x& = & 20+168 \\\Leftrightarrow & \color{red}{455} x& = & 188 \\\Leftrightarrow & x = \frac{188}{455} & & \\ & V = \left\{ \frac{188}{455} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{8})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{15}{8}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{+45} & = & \color{red}{168x} +80 \\\Leftrightarrow & 600x \color{red}{+45} \color{blue}{-45} \color{blue}{-168x} & = & \color{red}{168x} +80 \color{blue}{-168x} \color{blue}{-45} \\\Leftrightarrow & 600x-168x& = & 80-45 \\\Leftrightarrow & \color{red}{432} x& = & 35 \\\Leftrightarrow & x = \frac{35}{432} & & \\ & V = \left\{ \frac{35}{432} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-180} & = & \color{red}{-567x} +14 \\\Leftrightarrow & 630x \color{red}{-180} \color{blue}{+180} \color{blue}{+567x} & = & \color{red}{-567x} +14 \color{blue}{+567x} \color{blue}{+180} \\\Leftrightarrow & 630x+567x& = & 14+180 \\\Leftrightarrow & \color{red}{1197} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1197} & & \\ & V = \left\{ \frac{194}{1197} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{+80} & = & \color{red}{-252x} +63 \\\Leftrightarrow & -224x \color{red}{+80} \color{blue}{-80} \color{blue}{+252x} & = & \color{red}{-252x} +63 \color{blue}{+252x} \color{blue}{-80} \\\Leftrightarrow & -224x+252x& = & 63-80 \\\Leftrightarrow & \color{red}{28} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{28} & & \\ & V = \left\{ \frac{-17}{28} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{-441x} +49 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +49 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & -630x+441x& = & 49+90 \\\Leftrightarrow & \color{red}{-189} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-189} & & \\\Leftrightarrow & x = \frac{-139}{189} & & \\ & V = \left\{ \frac{-139}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & 7x+\frac{4}{7} \\\Leftrightarrow & 10x-\frac{8}{9}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-56} & = & \color{red}{441x} +36 \\\Leftrightarrow & 630x \color{red}{-56} \color{blue}{+56} \color{blue}{-441x} & = & \color{red}{441x} +36 \color{blue}{-441x} \color{blue}{+56} \\\Leftrightarrow & 630x-441x& = & 36+56 \\\Leftrightarrow & \color{red}{189} x& = & 92 \\\Leftrightarrow & x = \frac{92}{189} & & \\ & V = \left\{ \frac{92}{189} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x-\frac{24}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-216} & = & \color{red}{-441x} +14 \\\Leftrightarrow & -1890x \color{red}{-216} \color{blue}{+216} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+216} \\\Leftrightarrow & -1890x+441x& = & 14+216 \\\Leftrightarrow & \color{red}{-1449} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1449} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
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