Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-840}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -840x \color{red}{-105} & = & \color{red}{320x} +64 \\\Leftrightarrow & -840x \color{red}{-105} \color{blue}{+105} \color{blue}{-320x} & = & \color{red}{320x} +64 \color{blue}{-320x} \color{blue}{+105} \\\Leftrightarrow & -840x-320x& = & 64+105 \\\Leftrightarrow & \color{red}{-1160} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-1160} & & \\\Leftrightarrow & x = \frac{-169}{1160} & & \\ & V = \left\{ \frac{-169}{1160} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & -4x+\frac{8}{11} \\\Leftrightarrow & -15x+\frac{12}{5}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+132} & = & \color{red}{-220x} +40 \\\Leftrightarrow & -825x \color{red}{+132} \color{blue}{-132} \color{blue}{+220x} & = & \color{red}{-220x} +40 \color{blue}{+220x} \color{blue}{-132} \\\Leftrightarrow & -825x+220x& = & 40-132 \\\Leftrightarrow & \color{red}{-605} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-605} & & \\\Leftrightarrow & x = \frac{92}{605} & & \\ & V = \left\{ \frac{92}{605} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & 4x+\frac{7}{3} \\\Leftrightarrow & -15x-\frac{15}{11}& = & 4x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-45} & = & \color{red}{132x} +77 \\\Leftrightarrow & -495x \color{red}{-45} \color{blue}{+45} \color{blue}{-132x} & = & \color{red}{132x} +77 \color{blue}{-132x} \color{blue}{+45} \\\Leftrightarrow & -495x-132x& = & 77+45 \\\Leftrightarrow & \color{red}{-627} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-627} & & \\\Leftrightarrow & x = \frac{-122}{627} & & \\ & V = \left\{ \frac{-122}{627} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 7x+\frac{9}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{539x} +63 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +63 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & 1155x-539x& = & 63+66 \\\Leftrightarrow & \color{red}{616} x& = & 129 \\\Leftrightarrow & x = \frac{129}{616} & & \\ & V = \left\{ \frac{129}{616} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{3})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{16}{3}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{21x} +10 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{-21x} & = & \color{red}{21x} +10 \color{blue}{-21x} \color{blue}{-16} \\\Leftrightarrow & -48x-21x& = & 10-16 \\\Leftrightarrow & \color{red}{-69} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-69} & & \\\Leftrightarrow & x = \frac{2}{23} & & \\ & V = \left\{ \frac{2}{23} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{20}{9}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+100} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -900x \color{red}{+100} \color{blue}{-100} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-100} \\\Leftrightarrow & -900x+135x& = & 18-100 \\\Leftrightarrow & \color{red}{-765} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-765} & & \\\Leftrightarrow & x = \frac{82}{765} & & \\ & V = \left\{ \frac{82}{765} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{20}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-60} & = & \color{red}{147x} +28 \\\Leftrightarrow & -210x \color{red}{-60} \color{blue}{+60} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+60} \\\Leftrightarrow & -210x-147x& = & 28+60 \\\Leftrightarrow & \color{red}{-357} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-357} & & \\\Leftrightarrow & x = \frac{-88}{357} & & \\ & V = \left\{ \frac{-88}{357} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{1}{2})& = & -4x+\frac{5}{4} \\\Leftrightarrow & 35x-\frac{7}{2}& = & -4x+\frac{5}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{140}{ \color{blue}{4} }x- \frac{14}{ \color{blue}{4} })& = & (\frac{-16}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 140x \color{red}{-14} & = & \color{red}{-16x} +5 \\\Leftrightarrow & 140x \color{red}{-14} \color{blue}{+14} \color{blue}{+16x} & = & \color{red}{-16x} +5 \color{blue}{+16x} \color{blue}{+14} \\\Leftrightarrow & 140x+16x& = & 5+14 \\\Leftrightarrow & \color{red}{156} x& = & 19 \\\Leftrightarrow & x = \frac{19}{156} & & \\ & V = \left\{ \frac{19}{156} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{-54x} +5 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{-20} \\\Leftrightarrow & 60x+54x& = & 5-20 \\\Leftrightarrow & \color{red}{114} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{114} & & \\\Leftrightarrow & x = \frac{-5}{38} & & \\ & V = \left\{ \frac{-5}{38} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{11})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 30x+\frac{24}{11}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2970}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2970x \color{red}{+216} & = & \color{red}{693x} +55 \\\Leftrightarrow & 2970x \color{red}{+216} \color{blue}{-216} \color{blue}{-693x} & = & \color{red}{693x} +55 \color{blue}{-693x} \color{blue}{-216} \\\Leftrightarrow & 2970x-693x& = & 55-216 \\\Leftrightarrow & \color{red}{2277} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{2277} & & \\\Leftrightarrow & x = \frac{-7}{99} & & \\ & V = \left\{ \frac{-7}{99} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{4}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -10x+\frac{20}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+20} & = & \color{red}{63x} +30 \\\Leftrightarrow & -90x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -90x-63x& = & 30-20 \\\Leftrightarrow & \color{red}{-153} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-153} & & \\\Leftrightarrow & x = \frac{-10}{153} & & \\ & V = \left\{ \frac{-10}{153} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{3})& = & 3x+\frac{5}{2} \\\Leftrightarrow & -14x+\frac{28}{3}& = & 3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{56}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+56} & = & \color{red}{18x} +15 \\\Leftrightarrow & -84x \color{red}{+56} \color{blue}{-56} \color{blue}{-18x} & = & \color{red}{18x} +15 \color{blue}{-18x} \color{blue}{-56} \\\Leftrightarrow & -84x-18x& = & 15-56 \\\Leftrightarrow & \color{red}{-102} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-102} & & \\\Leftrightarrow & x = \frac{41}{102} & & \\ & V = \left\{ \frac{41}{102} \right\} & \\\end{align}\)
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