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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{5}{8} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+48} & = & \color{red}{392x} +35 \\\Leftrightarrow & -560x \color{red}{+48} \color{blue}{-48} \color{blue}{-392x} & = & \color{red}{392x} +35 \color{blue}{-392x} \color{blue}{-48} \\\Leftrightarrow & -560x-392x& = & 35-48 \\\Leftrightarrow & \color{red}{-952} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-952} & & \\\Leftrightarrow & x = \frac{13}{952} & & \\ & V = \left\{ \frac{13}{952} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & -5x+\frac{7}{12} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{2376}{ \color{blue}{132} }x+ \frac{216}{ \color{blue}{132} })& = & (\frac{-660}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 2376x \color{red}{+216} & = & \color{red}{-660x} +77 \\\Leftrightarrow & 2376x \color{red}{+216} \color{blue}{-216} \color{blue}{+660x} & = & \color{red}{-660x} +77 \color{blue}{+660x} \color{blue}{-216} \\\Leftrightarrow & 2376x+660x& = & 77-216 \\\Leftrightarrow & \color{red}{3036} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{3036} & & \\ & V = \left\{ \frac{-139}{3036} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{9})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{4}{9}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{+20} & = & \color{red}{-135x} +72 \\\Leftrightarrow & 450x \color{red}{+20} \color{blue}{-20} \color{blue}{+135x} & = & \color{red}{-135x} +72 \color{blue}{+135x} \color{blue}{-20} \\\Leftrightarrow & 450x+135x& = & 72-20 \\\Leftrightarrow & \color{red}{585} x& = & 52 \\\Leftrightarrow & x = \frac{52}{585} & & \\\Leftrightarrow & x = \frac{4}{45} & & \\ & V = \left\{ \frac{4}{45} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 25x-\frac{15}{4}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{-180x} +16 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{+180x} & = & \color{red}{-180x} +16 \color{blue}{+180x} \color{blue}{+75} \\\Leftrightarrow & 500x+180x& = & 16+75 \\\Leftrightarrow & \color{red}{680} x& = & 91 \\\Leftrightarrow & x = \frac{91}{680} & & \\ & V = \left\{ \frac{91}{680} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{3}{11})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -18x-\frac{18}{11}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1584}{ \color{blue}{88} }x- \frac{144}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1584x \color{red}{-144} & = & \color{red}{264x} +33 \\\Leftrightarrow & -1584x \color{red}{-144} \color{blue}{+144} \color{blue}{-264x} & = & \color{red}{264x} +33 \color{blue}{-264x} \color{blue}{+144} \\\Leftrightarrow & -1584x-264x& = & 33+144 \\\Leftrightarrow & \color{red}{-1848} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-1848} & & \\\Leftrightarrow & x = \frac{-59}{616} & & \\ & V = \left\{ \frac{-59}{616} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-6} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -84x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & -84x+35x& = & 9+6 \\\Leftrightarrow & \color{red}{-49} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-49} & & \\\Leftrightarrow & x = \frac{-15}{49} & & \\ & V = \left\{ \frac{-15}{49} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+126} & = & \color{red}{-539x} +88 \\\Leftrightarrow & -1848x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & -1848x+539x& = & 88-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1309} & & \\\Leftrightarrow & x = \frac{38}{1309} & & \\ & V = \left\{ \frac{38}{1309} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & 4x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{20}{7}& = & 4x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+20} & = & \color{red}{28x} +10 \\\Leftrightarrow & -105x \color{red}{+20} \color{blue}{-20} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{-20} \\\Leftrightarrow & -105x-28x& = & 10-20 \\\Leftrightarrow & \color{red}{-133} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-133} & & \\\Leftrightarrow & x = \frac{10}{133} & & \\ & V = \left\{ \frac{10}{133} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{2})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 14x+\frac{7}{2}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{56}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 56x \color{red}{+14} & = & \color{red}{20x} +3 \\\Leftrightarrow & 56x \color{red}{+14} \color{blue}{-14} \color{blue}{-20x} & = & \color{red}{20x} +3 \color{blue}{-20x} \color{blue}{-14} \\\Leftrightarrow & 56x-20x& = & 3-14 \\\Leftrightarrow & \color{red}{36} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{36} & & \\ & V = \left\{ \frac{-11}{36} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-30} \\\Leftrightarrow & -210x+49x& = & 10-30 \\\Leftrightarrow & \color{red}{-161} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-161} & & \\\Leftrightarrow & x = \frac{20}{161} & & \\ & V = \left\{ \frac{20}{161} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x- \frac{60}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{-60} & = & \color{red}{45x} +10 \\\Leftrightarrow & -108x \color{red}{-60} \color{blue}{+60} \color{blue}{-45x} & = & \color{red}{45x} +10 \color{blue}{-45x} \color{blue}{+60} \\\Leftrightarrow & -108x-45x& = & 10+60 \\\Leftrightarrow & \color{red}{-153} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-153} & & \\\Leftrightarrow & x = \frac{-70}{153} & & \\ & V = \left\{ \frac{-70}{153} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{11})& = & -5x+\frac{7}{6} \\\Leftrightarrow & 4x-\frac{8}{11}& = & -5x+\frac{7}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{264}{ \color{blue}{66} }x- \frac{48}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{77}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 264x \color{red}{-48} & = & \color{red}{-330x} +77 \\\Leftrightarrow & 264x \color{red}{-48} \color{blue}{+48} \color{blue}{+330x} & = & \color{red}{-330x} +77 \color{blue}{+330x} \color{blue}{+48} \\\Leftrightarrow & 264x+330x& = & 77+48 \\\Leftrightarrow & \color{red}{594} x& = & 125 \\\Leftrightarrow & x = \frac{125}{594} & & \\ & V = \left\{ \frac{125}{594} \right\} & \\\end{align}\)
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