Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{60}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-60} & = & \color{red}{-378x} +35 \\\Leftrightarrow & -840x \color{red}{-60} \color{blue}{+60} \color{blue}{+378x} & = & \color{red}{-378x} +35 \color{blue}{+378x} \color{blue}{+60} \\\Leftrightarrow & -840x+378x& = & 35+60 \\\Leftrightarrow & \color{red}{-462} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-462} & & \\\Leftrightarrow & x = \frac{-95}{462} & & \\ & V = \left\{ \frac{-95}{462} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-126}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -126x \color{red}{+42} & = & \color{red}{-27x} +8 \\\Leftrightarrow & -126x \color{red}{+42} \color{blue}{-42} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-42} \\\Leftrightarrow & -126x+27x& = & 8-42 \\\Leftrightarrow & \color{red}{-99} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-99} & & \\\Leftrightarrow & x = \frac{34}{99} & & \\ & V = \left\{ \frac{34}{99} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -10x+\frac{15}{2}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+105} & = & \color{red}{-98x} +6 \\\Leftrightarrow & -140x \color{red}{+105} \color{blue}{-105} \color{blue}{+98x} & = & \color{red}{-98x} +6 \color{blue}{+98x} \color{blue}{-105} \\\Leftrightarrow & -140x+98x& = & 6-105 \\\Leftrightarrow & \color{red}{-42} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{-42} & & \\\Leftrightarrow & x = \frac{33}{14} & & \\ & V = \left\{ \frac{33}{14} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{8}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-24} & = & \color{red}{231x} +110 \\\Leftrightarrow & 660x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & 660x-231x& = & 110+24 \\\Leftrightarrow & \color{red}{429} x& = & 134 \\\Leftrightarrow & x = \frac{134}{429} & & \\ & V = \left\{ \frac{134}{429} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{11})& = & 7x+\frac{9}{5} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-120} & = & \color{red}{385x} +99 \\\Leftrightarrow & -1650x \color{red}{-120} \color{blue}{+120} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{+120} \\\Leftrightarrow & -1650x-385x& = & 99+120 \\\Leftrightarrow & \color{red}{-2035} x& = & 219 \\\Leftrightarrow & x = \frac{219}{-2035} & & \\\Leftrightarrow & x = \frac{-219}{2035} & & \\ & V = \left\{ \frac{-219}{2035} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{105x} +50 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+54} \\\Leftrightarrow & -360x-105x& = & 50+54 \\\Leftrightarrow & \color{red}{-465} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-465} & & \\\Leftrightarrow & x = \frac{-104}{465} & & \\ & V = \left\{ \frac{-104}{465} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 6x+\frac{10}{11} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1100}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{264}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1100x \color{red}{-165} & = & \color{red}{264x} +40 \\\Leftrightarrow & -1100x \color{red}{-165} \color{blue}{+165} \color{blue}{-264x} & = & \color{red}{264x} +40 \color{blue}{-264x} \color{blue}{+165} \\\Leftrightarrow & -1100x-264x& = & 40+165 \\\Leftrightarrow & \color{red}{-1364} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-1364} & & \\\Leftrightarrow & x = \frac{-205}{1364} & & \\ & V = \left\{ \frac{-205}{1364} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & -126x-147x& = & 56+18 \\\Leftrightarrow & \color{red}{-273} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-273} & & \\\Leftrightarrow & x = \frac{-74}{273} & & \\ & V = \left\{ \frac{-74}{273} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{8})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{9}{8}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-280x} +32 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+280x} & = & \color{red}{-280x} +32 \color{blue}{+280x} \color{blue}{-63} \\\Leftrightarrow & 336x+280x& = & 32-63 \\\Leftrightarrow & \color{red}{616} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{616} & & \\ & V = \left\{ \frac{-31}{616} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{10})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -28x-\frac{21}{10}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x- \frac{21}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{-90x} +4 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{+90x} & = & \color{red}{-90x} +4 \color{blue}{+90x} \color{blue}{+21} \\\Leftrightarrow & -280x+90x& = & 4+21 \\\Leftrightarrow & \color{red}{-190} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-190} & & \\\Leftrightarrow & x = \frac{-5}{38} & & \\ & V = \left\{ \frac{-5}{38} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{11})& = & -3x+\frac{3}{5} \\\Leftrightarrow & -20x+\frac{25}{11}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+125} & = & \color{red}{-165x} +33 \\\Leftrightarrow & -1100x \color{red}{+125} \color{blue}{-125} \color{blue}{+165x} & = & \color{red}{-165x} +33 \color{blue}{+165x} \color{blue}{-125} \\\Leftrightarrow & -1100x+165x& = & 33-125 \\\Leftrightarrow & \color{red}{-935} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{-935} & & \\\Leftrightarrow & x = \frac{92}{935} & & \\ & V = \left\{ \frac{92}{935} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -9x+\frac{5}{9} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -9x+\frac{5}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{2016}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{40}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 2016x \color{red}{-189} & = & \color{red}{-648x} +40 \\\Leftrightarrow & 2016x \color{red}{-189} \color{blue}{+189} \color{blue}{+648x} & = & \color{red}{-648x} +40 \color{blue}{+648x} \color{blue}{+189} \\\Leftrightarrow & 2016x+648x& = & 40+189 \\\Leftrightarrow & \color{red}{2664} x& = & 229 \\\Leftrightarrow & x = \frac{229}{2664} & & \\ & V = \left\{ \frac{229}{2664} \right\} & \\\end{align}\)
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