Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{4})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{21}{4}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{280}{ \color{blue}{20} }x- \frac{105}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 280x \color{red}{-105} & = & \color{red}{60x} +24 \\\Leftrightarrow & 280x \color{red}{-105} \color{blue}{+105} \color{blue}{-60x} & = & \color{red}{60x} +24 \color{blue}{-60x} \color{blue}{+105} \\\Leftrightarrow & 280x-60x& = & 24+105 \\\Leftrightarrow & \color{red}{220} x& = & 129 \\\Leftrightarrow & x = \frac{129}{220} & & \\ & V = \left\{ \frac{129}{220} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{11})& = & 2x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{25}{11}& = & 2x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{165}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 165x \color{red}{-25} & = & \color{red}{22x} +7 \\\Leftrightarrow & 165x \color{red}{-25} \color{blue}{+25} \color{blue}{-22x} & = & \color{red}{22x} +7 \color{blue}{-22x} \color{blue}{+25} \\\Leftrightarrow & 165x-22x& = & 7+25 \\\Leftrightarrow & \color{red}{143} x& = & 32 \\\Leftrightarrow & x = \frac{32}{143} & & \\ & V = \left\{ \frac{32}{143} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{9})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{4}{9}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-44} & = & \color{red}{-693x} +90 \\\Leftrightarrow & -990x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +90 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & -990x+693x& = & 90+44 \\\Leftrightarrow & \color{red}{-297} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-297} & & \\\Leftrightarrow & x = \frac{-134}{297} & & \\ & V = \left\{ \frac{-134}{297} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{5}{2})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 35x-\frac{35}{2}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x- \frac{140}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{-140} & = & \color{red}{24x} +7 \\\Leftrightarrow & 280x \color{red}{-140} \color{blue}{+140} \color{blue}{-24x} & = & \color{red}{24x} +7 \color{blue}{-24x} \color{blue}{+140} \\\Leftrightarrow & 280x-24x& = & 7+140 \\\Leftrightarrow & \color{red}{256} x& = & 147 \\\Leftrightarrow & x = \frac{147}{256} & & \\ & V = \left\{ \frac{147}{256} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x-\frac{9}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-99} & = & \color{red}{-385x} +10 \\\Leftrightarrow & -330x \color{red}{-99} \color{blue}{+99} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+99} \\\Leftrightarrow & -330x+385x& = & 10+99 \\\Leftrightarrow & \color{red}{55} x& = & 109 \\\Leftrightarrow & x = \frac{109}{55} & & \\ & V = \left\{ \frac{109}{55} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{9})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{25}{9}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x+ \frac{50}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{+50} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 360x \color{red}{+50} \color{blue}{-50} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-50} \\\Leftrightarrow & 360x+54x& = & 27-50 \\\Leftrightarrow & \color{red}{414} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{414} & & \\\Leftrightarrow & x = \frac{-1}{18} & & \\ & V = \left\{ \frac{-1}{18} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{10}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+10} & = & \color{red}{-77x} +2 \\\Leftrightarrow & -66x \color{red}{+10} \color{blue}{-10} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-10} \\\Leftrightarrow & -66x+77x& = & 2-10 \\\Leftrightarrow & \color{red}{11} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{11} & & \\ & V = \left\{ \frac{-8}{11} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{5})& = & 5x+\frac{2}{9} \\\Leftrightarrow & 6x-\frac{6}{5}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{270}{ \color{blue}{45} }x- \frac{54}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 270x \color{red}{-54} & = & \color{red}{225x} +10 \\\Leftrightarrow & 270x \color{red}{-54} \color{blue}{+54} \color{blue}{-225x} & = & \color{red}{225x} +10 \color{blue}{-225x} \color{blue}{+54} \\\Leftrightarrow & 270x-225x& = & 10+54 \\\Leftrightarrow & \color{red}{45} x& = & 64 \\\Leftrightarrow & x = \frac{64}{45} & & \\ & V = \left\{ \frac{64}{45} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-240}{ \color{blue}{40} }x- \frac{48}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{280x} +35 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+48} \\\Leftrightarrow & -240x-280x& = & 35+48 \\\Leftrightarrow & \color{red}{-520} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-520} & & \\\Leftrightarrow & x = \frac{-83}{520} & & \\ & V = \left\{ \frac{-83}{520} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{-245x} +45 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 525x+245x& = & 45+84 \\\Leftrightarrow & \color{red}{770} x& = & 129 \\\Leftrightarrow & x = \frac{129}{770} & & \\ & V = \left\{ \frac{129}{770} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-54} & = & \color{red}{-441x} +14 \\\Leftrightarrow & 504x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +14 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & 504x+441x& = & 14+54 \\\Leftrightarrow & \color{red}{945} x& = & 68 \\\Leftrightarrow & x = \frac{68}{945} & & \\ & V = \left\{ \frac{68}{945} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 8x+\frac{4}{9} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{72x} +4 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{-42} \\\Leftrightarrow & 315x-72x& = & 4-42 \\\Leftrightarrow & \color{red}{243} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{243} & & \\ & V = \left\{ \frac{-38}{243} \right\} & \\\end{align}\)
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