Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{2})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -28x-\frac{21}{2}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x- \frac{63}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{-63} & = & \color{red}{-48x} +4 \\\Leftrightarrow & -168x \color{red}{-63} \color{blue}{+63} \color{blue}{+48x} & = & \color{red}{-48x} +4 \color{blue}{+48x} \color{blue}{+63} \\\Leftrightarrow & -168x+48x& = & 4+63 \\\Leftrightarrow & \color{red}{-120} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-120} & & \\\Leftrightarrow & x = \frac{-67}{120} & & \\ & V = \left\{ \frac{-67}{120} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 15x+\frac{20}{11}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+140} & = & \color{red}{539x} +22 \\\Leftrightarrow & 1155x \color{red}{+140} \color{blue}{-140} \color{blue}{-539x} & = & \color{red}{539x} +22 \color{blue}{-539x} \color{blue}{-140} \\\Leftrightarrow & 1155x-539x& = & 22-140 \\\Leftrightarrow & \color{red}{616} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{616} & & \\\Leftrightarrow & x = \frac{-59}{308} & & \\ & V = \left\{ \frac{-59}{308} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{11})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -10x-\frac{6}{11}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-18} & = & \color{red}{-231x} +77 \\\Leftrightarrow & -330x \color{red}{-18} \color{blue}{+18} \color{blue}{+231x} & = & \color{red}{-231x} +77 \color{blue}{+231x} \color{blue}{+18} \\\Leftrightarrow & -330x+231x& = & 77+18 \\\Leftrightarrow & \color{red}{-99} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-99} & & \\\Leftrightarrow & x = \frac{-95}{99} & & \\ & V = \left\{ \frac{-95}{99} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & -7x+\frac{5}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{-441x} +35 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{+441x} & = & \color{red}{-441x} +35 \color{blue}{+441x} \color{blue}{+90} \\\Leftrightarrow & 630x+441x& = & 35+90 \\\Leftrightarrow & \color{red}{1071} x& = & 125 \\\Leftrightarrow & x = \frac{125}{1071} & & \\ & V = \left\{ \frac{125}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{5})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -16x+\frac{16}{5}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-640}{ \color{blue}{40} }x+ \frac{128}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -640x \color{red}{+128} & = & \color{red}{280x} +45 \\\Leftrightarrow & -640x \color{red}{+128} \color{blue}{-128} \color{blue}{-280x} & = & \color{red}{280x} +45 \color{blue}{-280x} \color{blue}{-128} \\\Leftrightarrow & -640x-280x& = & 45-128 \\\Leftrightarrow & \color{red}{-920} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-920} & & \\\Leftrightarrow & x = \frac{83}{920} & & \\ & V = \left\{ \frac{83}{920} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-90} & = & \color{red}{147x} +49 \\\Leftrightarrow & 378x \color{red}{-90} \color{blue}{+90} \color{blue}{-147x} & = & \color{red}{147x} +49 \color{blue}{-147x} \color{blue}{+90} \\\Leftrightarrow & 378x-147x& = & 49+90 \\\Leftrightarrow & \color{red}{231} x& = & 139 \\\Leftrightarrow & x = \frac{139}{231} & & \\ & V = \left\{ \frac{139}{231} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-9} & = & \color{red}{25x} +6 \\\Leftrightarrow & 30x \color{red}{-9} \color{blue}{+9} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+9} \\\Leftrightarrow & 30x-25x& = & 6+9 \\\Leftrightarrow & \color{red}{5} x& = & 15 \\\Leftrightarrow & x = \frac{15}{5} & & \\\Leftrightarrow & x = 3 & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{3}{5} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x+ \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{+90} & = & \color{red}{275x} +33 \\\Leftrightarrow & -1320x \color{red}{+90} \color{blue}{-90} \color{blue}{-275x} & = & \color{red}{275x} +33 \color{blue}{-275x} \color{blue}{-90} \\\Leftrightarrow & -1320x-275x& = & 33-90 \\\Leftrightarrow & \color{red}{-1595} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-1595} & & \\\Leftrightarrow & x = \frac{57}{1595} & & \\ & V = \left\{ \frac{57}{1595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{9})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -14x+\frac{14}{9}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+154} & = & \color{red}{297x} +36 \\\Leftrightarrow & -1386x \color{red}{+154} \color{blue}{-154} \color{blue}{-297x} & = & \color{red}{297x} +36 \color{blue}{-297x} \color{blue}{-154} \\\Leftrightarrow & -1386x-297x& = & 36-154 \\\Leftrightarrow & \color{red}{-1683} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-1683} & & \\\Leftrightarrow & x = \frac{118}{1683} & & \\ & V = \left\{ \frac{118}{1683} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{+12} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -45x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -45x+35x& = & 6-12 \\\Leftrightarrow & \color{red}{-10} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-10} & & \\\Leftrightarrow & x = \frac{3}{5} & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & 3x+\frac{3}{8} \\\Leftrightarrow & -20x+\frac{15}{8}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-160}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -160x \color{red}{+15} & = & \color{red}{24x} +3 \\\Leftrightarrow & -160x \color{red}{+15} \color{blue}{-15} \color{blue}{-24x} & = & \color{red}{24x} +3 \color{blue}{-24x} \color{blue}{-15} \\\Leftrightarrow & -160x-24x& = & 3-15 \\\Leftrightarrow & \color{red}{-184} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-184} & & \\\Leftrightarrow & x = \frac{3}{46} & & \\ & V = \left\{ \frac{3}{46} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{-105x} +50 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-72} \\\Leftrightarrow & 450x+105x& = & 50-72 \\\Leftrightarrow & \color{red}{555} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{555} & & \\ & V = \left\{ \frac{-22}{555} \right\} & \\\end{align}\)
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