Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -3x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & -168x+63x& = & 6-140 \\\Leftrightarrow & \color{red}{-105} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{-105} & & \\\Leftrightarrow & x = \frac{134}{105} & & \\ & V = \left\{ \frac{134}{105} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 8x-\frac{6}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+18} \\\Leftrightarrow & 120x+75x& = & 20+18 \\\Leftrightarrow & \color{red}{195} x& = & 38 \\\Leftrightarrow & x = \frac{38}{195} & & \\ & V = \left\{ \frac{38}{195} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{4}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+32} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -280x \color{red}{+32} \color{blue}{-32} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-32} \\\Leftrightarrow & -280x+98x& = & 63-32 \\\Leftrightarrow & \color{red}{-182} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-182} & & \\\Leftrightarrow & x = \frac{-31}{182} & & \\ & V = \left\{ \frac{-31}{182} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -4x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{-165} & = & \color{red}{-176x} +24 \\\Leftrightarrow & 660x \color{red}{-165} \color{blue}{+165} \color{blue}{+176x} & = & \color{red}{-176x} +24 \color{blue}{+176x} \color{blue}{+165} \\\Leftrightarrow & 660x+176x& = & 24+165 \\\Leftrightarrow & \color{red}{836} x& = & 189 \\\Leftrightarrow & x = \frac{189}{836} & & \\ & V = \left\{ \frac{189}{836} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{7})& = & 9x+\frac{3}{11} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-176} & = & \color{red}{693x} +21 \\\Leftrightarrow & -616x \color{red}{-176} \color{blue}{+176} \color{blue}{-693x} & = & \color{red}{693x} +21 \color{blue}{-693x} \color{blue}{+176} \\\Leftrightarrow & -616x-693x& = & 21+176 \\\Leftrightarrow & \color{red}{-1309} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-1309} & & \\\Leftrightarrow & x = \frac{-197}{1309} & & \\ & V = \left\{ \frac{-197}{1309} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{9})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -10x-\frac{4}{9}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-4} & = & \color{red}{63x} +5 \\\Leftrightarrow & -90x \color{red}{-4} \color{blue}{+4} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{+4} \\\Leftrightarrow & -90x-63x& = & 5+4 \\\Leftrightarrow & \color{red}{-153} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-153} & & \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 28x-\frac{28}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1540}{ \color{blue}{55} }x- \frac{140}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1540x \color{red}{-140} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 1540x \color{red}{-140} \color{blue}{+140} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+140} \\\Leftrightarrow & 1540x+275x& = & 66+140 \\\Leftrightarrow & \color{red}{1815} x& = & 206 \\\Leftrightarrow & x = \frac{206}{1815} & & \\ & V = \left\{ \frac{206}{1815} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+12} & = & \color{red}{-50x} +45 \\\Leftrightarrow & 60x \color{red}{+12} \color{blue}{-12} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-12} \\\Leftrightarrow & 60x+50x& = & 45-12 \\\Leftrightarrow & \color{red}{110} x& = & 33 \\\Leftrightarrow & x = \frac{33}{110} & & \\\Leftrightarrow & x = \frac{3}{10} & & \\ & V = \left\{ \frac{3}{10} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{5})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{+14} & = & \color{red}{-45x} +6 \\\Leftrightarrow & -175x \color{red}{+14} \color{blue}{-14} \color{blue}{+45x} & = & \color{red}{-45x} +6 \color{blue}{+45x} \color{blue}{-14} \\\Leftrightarrow & -175x+45x& = & 6-14 \\\Leftrightarrow & \color{red}{-130} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-130} & & \\\Leftrightarrow & x = \frac{4}{65} & & \\ & V = \left\{ \frac{4}{65} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{4}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 15x-\frac{20}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{-20} & = & \color{red}{49x} +8 \\\Leftrightarrow & 105x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & 105x-49x& = & 8+20 \\\Leftrightarrow & \color{red}{56} x& = & 28 \\\Leftrightarrow & x = \frac{28}{56} & & \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x+ \frac{40}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{-18x} +15 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{+18x} & = & \color{red}{-18x} +15 \color{blue}{+18x} \color{blue}{-40} \\\Leftrightarrow & 120x+18x& = & 15-40 \\\Leftrightarrow & \color{red}{138} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{138} & & \\ & V = \left\{ \frac{-25}{138} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{1}{2})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -20x+\frac{5}{2}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{10}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+15} & = & \color{red}{-42x} +10 \\\Leftrightarrow & -120x \color{red}{+15} \color{blue}{-15} \color{blue}{+42x} & = & \color{red}{-42x} +10 \color{blue}{+42x} \color{blue}{-15} \\\Leftrightarrow & -120x+42x& = & 10-15 \\\Leftrightarrow & \color{red}{-78} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-78} & & \\\Leftrightarrow & x = \frac{5}{78} & & \\ & V = \left\{ \frac{5}{78} \right\} & \\\end{align}\)
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