Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -20x-\frac{8}{9}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-88} & = & \color{red}{-693x} +72 \\\Leftrightarrow & -1980x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +72 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -1980x+693x& = & 72+88 \\\Leftrightarrow & \color{red}{-1287} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-1287} & & \\\Leftrightarrow & x = \frac{-160}{1287} & & \\ & V = \left\{ \frac{-160}{1287} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{378}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 378x \color{red}{+56} & = & \color{red}{-441x} +18 \\\Leftrightarrow & 378x \color{red}{+56} \color{blue}{-56} \color{blue}{+441x} & = & \color{red}{-441x} +18 \color{blue}{+441x} \color{blue}{-56} \\\Leftrightarrow & 378x+441x& = & 18-56 \\\Leftrightarrow & \color{red}{819} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{819} & & \\ & V = \left\{ \frac{-38}{819} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{7})& = & 5x+\frac{7}{12} \\\Leftrightarrow & -4x-\frac{4}{7}& = & 5x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-336}{ \color{blue}{84} }x- \frac{48}{ \color{blue}{84} })& = & (\frac{420}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{420x} +49 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-420x} & = & \color{red}{420x} +49 \color{blue}{-420x} \color{blue}{+48} \\\Leftrightarrow & -336x-420x& = & 49+48 \\\Leftrightarrow & \color{red}{-756} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-756} & & \\\Leftrightarrow & x = \frac{-97}{756} & & \\ & V = \left\{ \frac{-97}{756} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & 8x+\frac{5}{9} \\\Leftrightarrow & -21x+\frac{21}{8}& = & 8x+\frac{5}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x+ \frac{189}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{40}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{+189} & = & \color{red}{576x} +40 \\\Leftrightarrow & -1512x \color{red}{+189} \color{blue}{-189} \color{blue}{-576x} & = & \color{red}{576x} +40 \color{blue}{-576x} \color{blue}{-189} \\\Leftrightarrow & -1512x-576x& = & 40-189 \\\Leftrightarrow & \color{red}{-2088} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{-2088} & & \\\Leftrightarrow & x = \frac{149}{2088} & & \\ & V = \left\{ \frac{149}{2088} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{3}{10})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x-\frac{9}{10}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x- \frac{18}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{-18} & = & \color{red}{-140x} +15 \\\Leftrightarrow & -120x \color{red}{-18} \color{blue}{+18} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{+18} \\\Leftrightarrow & -120x+140x& = & 15+18 \\\Leftrightarrow & \color{red}{20} x& = & 33 \\\Leftrightarrow & x = \frac{33}{20} & & \\ & V = \left\{ \frac{33}{20} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{4}{3})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -25x-\frac{20}{3}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-150}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{30}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -150x \color{red}{-40} & = & \color{red}{30x} +27 \\\Leftrightarrow & -150x \color{red}{-40} \color{blue}{+40} \color{blue}{-30x} & = & \color{red}{30x} +27 \color{blue}{-30x} \color{blue}{+40} \\\Leftrightarrow & -150x-30x& = & 27+40 \\\Leftrightarrow & \color{red}{-180} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-180} & & \\\Leftrightarrow & x = \frac{-67}{180} & & \\ & V = \left\{ \frac{-67}{180} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{9})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{4}{9}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-4} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -90x \color{red}{-4} \color{blue}{+4} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{+4} \\\Leftrightarrow & -90x+63x& = & 12+4 \\\Leftrightarrow & \color{red}{-27} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-27} & & \\\Leftrightarrow & x = \frac{-16}{27} & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & -3x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{16}{7}& = & -3x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{96}{ \color{blue}{42} })& = & (\frac{-126}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-96} & = & \color{red}{-126x} +35 \\\Leftrightarrow & -840x \color{red}{-96} \color{blue}{+96} \color{blue}{+126x} & = & \color{red}{-126x} +35 \color{blue}{+126x} \color{blue}{+96} \\\Leftrightarrow & -840x+126x& = & 35+96 \\\Leftrightarrow & \color{red}{-714} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-714} & & \\\Leftrightarrow & x = \frac{-131}{714} & & \\ & V = \left\{ \frac{-131}{714} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{5}{7})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -10x-\frac{25}{7}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{50}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-50} & = & \color{red}{-98x} +35 \\\Leftrightarrow & -140x \color{red}{-50} \color{blue}{+50} \color{blue}{+98x} & = & \color{red}{-98x} +35 \color{blue}{+98x} \color{blue}{+50} \\\Leftrightarrow & -140x+98x& = & 35+50 \\\Leftrightarrow & \color{red}{-42} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-42} & & \\\Leftrightarrow & x = \frac{-85}{42} & & \\ & V = \left\{ \frac{-85}{42} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{7})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -20x+\frac{8}{7}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{+64} & = & \color{red}{168x} +21 \\\Leftrightarrow & -1120x \color{red}{+64} \color{blue}{-64} \color{blue}{-168x} & = & \color{red}{168x} +21 \color{blue}{-168x} \color{blue}{-64} \\\Leftrightarrow & -1120x-168x& = & 21-64 \\\Leftrightarrow & \color{red}{-1288} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-1288} & & \\\Leftrightarrow & x = \frac{43}{1288} & & \\ & V = \left\{ \frac{43}{1288} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{11})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{11}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{770}{ \color{blue}{55} }x- \frac{175}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 770x \color{red}{-175} & = & \color{red}{-165x} +66 \\\Leftrightarrow & 770x \color{red}{-175} \color{blue}{+175} \color{blue}{+165x} & = & \color{red}{-165x} +66 \color{blue}{+165x} \color{blue}{+175} \\\Leftrightarrow & 770x+165x& = & 66+175 \\\Leftrightarrow & \color{red}{935} x& = & 241 \\\Leftrightarrow & x = \frac{241}{935} & & \\ & V = \left\{ \frac{241}{935} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{5})& = & 8x+\frac{7}{6} \\\Leftrightarrow & -15x-\frac{12}{5}& = & 8x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-450}{ \color{blue}{30} }x- \frac{72}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -450x \color{red}{-72} & = & \color{red}{240x} +35 \\\Leftrightarrow & -450x \color{red}{-72} \color{blue}{+72} \color{blue}{-240x} & = & \color{red}{240x} +35 \color{blue}{-240x} \color{blue}{+72} \\\Leftrightarrow & -450x-240x& = & 35+72 \\\Leftrightarrow & \color{red}{-690} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-690} & & \\\Leftrightarrow & x = \frac{-107}{690} & & \\ & V = \left\{ \frac{-107}{690} \right\} & \\\end{align}\)
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