Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{4})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{8}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-75} & = & \color{red}{-100x} +8 \\\Leftrightarrow & -180x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +8 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & -180x+100x& = & 8+75 \\\Leftrightarrow & \color{red}{-80} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-80} & & \\\Leftrightarrow & x = \frac{-83}{80} & & \\ & V = \left\{ \frac{-83}{80} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-30} & = & \color{red}{315x} +42 \\\Leftrightarrow & 350x \color{red}{-30} \color{blue}{+30} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+30} \\\Leftrightarrow & 350x-315x& = & 42+30 \\\Leftrightarrow & \color{red}{35} x& = & 72 \\\Leftrightarrow & x = \frac{72}{35} & & \\ & V = \left\{ \frac{72}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 10x-\frac{25}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{225}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-225} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 630x \color{red}{-225} \color{blue}{+225} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+225} \\\Leftrightarrow & 630x+441x& = & 14+225 \\\Leftrightarrow & \color{red}{1071} x& = & 239 \\\Leftrightarrow & x = \frac{239}{1071} & & \\ & V = \left\{ \frac{239}{1071} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 6x-\frac{4}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-28} & = & \color{red}{385x} +88 \\\Leftrightarrow & 462x \color{red}{-28} \color{blue}{+28} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+28} \\\Leftrightarrow & 462x-385x& = & 88+28 \\\Leftrightarrow & \color{red}{77} x& = & 116 \\\Leftrightarrow & x = \frac{116}{77} & & \\ & V = \left\{ \frac{116}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{9})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{8}{9}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{-8} & = & \color{red}{-45x} +12 \\\Leftrightarrow & -108x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +12 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & -108x+45x& = & 12+8 \\\Leftrightarrow & \color{red}{-63} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-63} & & \\\Leftrightarrow & x = \frac{-20}{63} & & \\ & V = \left\{ \frac{-20}{63} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{3})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{297x} +12 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{-297x} & = & \color{red}{297x} +12 \color{blue}{-297x} \color{blue}{+220} \\\Leftrightarrow & 660x-297x& = & 12+220 \\\Leftrightarrow & \color{red}{363} x& = & 232 \\\Leftrightarrow & x = \frac{232}{363} & & \\ & V = \left\{ \frac{232}{363} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{9})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-80} & = & \color{red}{108x} +27 \\\Leftrightarrow & 720x \color{red}{-80} \color{blue}{+80} \color{blue}{-108x} & = & \color{red}{108x} +27 \color{blue}{-108x} \color{blue}{+80} \\\Leftrightarrow & 720x-108x& = & 27+80 \\\Leftrightarrow & \color{red}{612} x& = & 107 \\\Leftrightarrow & x = \frac{107}{612} & & \\ & V = \left\{ \frac{107}{612} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & -3x+\frac{10}{3} \\\Leftrightarrow & 16x+\frac{8}{9}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{+8} & = & \color{red}{-27x} +30 \\\Leftrightarrow & 144x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +30 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & 144x+27x& = & 30-8 \\\Leftrightarrow & \color{red}{171} x& = & 22 \\\Leftrightarrow & x = \frac{22}{171} & & \\ & V = \left\{ \frac{22}{171} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & -4x+\frac{7}{9} \\\Leftrightarrow & -15x-\frac{10}{7}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-90} & = & \color{red}{-252x} +49 \\\Leftrightarrow & -945x \color{red}{-90} \color{blue}{+90} \color{blue}{+252x} & = & \color{red}{-252x} +49 \color{blue}{+252x} \color{blue}{+90} \\\Leftrightarrow & -945x+252x& = & 49+90 \\\Leftrightarrow & \color{red}{-693} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-693} & & \\\Leftrightarrow & x = \frac{-139}{693} & & \\ & V = \left\{ \frac{-139}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-60} & = & \color{red}{-70x} +21 \\\Leftrightarrow & 168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +21 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & 168x+70x& = & 21+60 \\\Leftrightarrow & \color{red}{238} x& = & 81 \\\Leftrightarrow & x = \frac{81}{238} & & \\ & V = \left\{ \frac{81}{238} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-72} & = & \color{red}{-75x} +10 \\\Leftrightarrow & 180x \color{red}{-72} \color{blue}{+72} \color{blue}{+75x} & = & \color{red}{-75x} +10 \color{blue}{+75x} \color{blue}{+72} \\\Leftrightarrow & 180x+75x& = & 10+72 \\\Leftrightarrow & \color{red}{255} x& = & 82 \\\Leftrightarrow & x = \frac{82}{255} & & \\ & V = \left\{ \frac{82}{255} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{7})& = & 4x+\frac{9}{7} \\\Leftrightarrow & 15x+\frac{20}{7}& = & 4x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+20} & = & \color{red}{28x} +9 \\\Leftrightarrow & 105x \color{red}{+20} \color{blue}{-20} \color{blue}{-28x} & = & \color{red}{28x} +9 \color{blue}{-28x} \color{blue}{-20} \\\Leftrightarrow & 105x-28x& = & 9-20 \\\Leftrightarrow & \color{red}{77} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{77} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
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