Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-792}{ \color{blue}{132} }x+ \frac{180}{ \color{blue}{132} })& = & (\frac{924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -792x \color{red}{+180} & = & \color{red}{924x} +55 \\\Leftrightarrow & -792x \color{red}{+180} \color{blue}{-180} \color{blue}{-924x} & = & \color{red}{924x} +55 \color{blue}{-924x} \color{blue}{-180} \\\Leftrightarrow & -792x-924x& = & 55-180 \\\Leftrightarrow & \color{red}{-1716} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-1716} & & \\\Leftrightarrow & x = \frac{125}{1716} & & \\ & V = \left\{ \frac{125}{1716} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{15}{11}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+30} & = & \color{red}{-66x} +33 \\\Leftrightarrow & 550x \color{red}{+30} \color{blue}{-30} \color{blue}{+66x} & = & \color{red}{-66x} +33 \color{blue}{+66x} \color{blue}{-30} \\\Leftrightarrow & 550x+66x& = & 33-30 \\\Leftrightarrow & \color{red}{616} x& = & 3 \\\Leftrightarrow & x = \frac{3}{616} & & \\ & V = \left\{ \frac{3}{616} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{5})& = & -3x+\frac{3}{10} \\\Leftrightarrow & -8x-\frac{8}{5}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{16}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-16} & = & \color{red}{-30x} +3 \\\Leftrightarrow & -80x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +3 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & -80x+30x& = & 3+16 \\\Leftrightarrow & \color{red}{-50} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-50} & & \\\Leftrightarrow & x = \frac{-19}{50} & & \\ & V = \left\{ \frac{-19}{50} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{9})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{-28} & = & \color{red}{315x} +81 \\\Leftrightarrow & 504x \color{red}{-28} \color{blue}{+28} \color{blue}{-315x} & = & \color{red}{315x} +81 \color{blue}{-315x} \color{blue}{+28} \\\Leftrightarrow & 504x-315x& = & 81+28 \\\Leftrightarrow & \color{red}{189} x& = & 109 \\\Leftrightarrow & x = \frac{109}{189} & & \\ & V = \left\{ \frac{109}{189} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{24}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-24} & = & \color{red}{-154x} +55 \\\Leftrightarrow & 440x \color{red}{-24} \color{blue}{+24} \color{blue}{+154x} & = & \color{red}{-154x} +55 \color{blue}{+154x} \color{blue}{+24} \\\Leftrightarrow & 440x+154x& = & 55+24 \\\Leftrightarrow & \color{red}{594} x& = & 79 \\\Leftrightarrow & x = \frac{79}{594} & & \\ & V = \left\{ \frac{79}{594} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 10x-\frac{25}{6}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{-125} & = & \color{red}{-210x} +24 \\\Leftrightarrow & 300x \color{red}{-125} \color{blue}{+125} \color{blue}{+210x} & = & \color{red}{-210x} +24 \color{blue}{+210x} \color{blue}{+125} \\\Leftrightarrow & 300x+210x& = & 24+125 \\\Leftrightarrow & \color{red}{510} x& = & 149 \\\Leftrightarrow & x = \frac{149}{510} & & \\ & V = \left\{ \frac{149}{510} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{2})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{15}{2}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-24}{ \color{blue}{2} }x- \frac{15}{ \color{blue}{2} })& = & (\frac{-10}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -24x \color{red}{-15} & = & \color{red}{-10x} +5 \\\Leftrightarrow & -24x \color{red}{-15} \color{blue}{+15} \color{blue}{+10x} & = & \color{red}{-10x} +5 \color{blue}{+10x} \color{blue}{+15} \\\Leftrightarrow & -24x+10x& = & 5+15 \\\Leftrightarrow & \color{red}{-14} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-14} & & \\\Leftrightarrow & x = \frac{-10}{7} & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -8x-\frac{6}{5}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{-90x} +35 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{+90x} & = & \color{red}{-90x} +35 \color{blue}{+90x} \color{blue}{+12} \\\Leftrightarrow & -80x+90x& = & 35+12 \\\Leftrightarrow & \color{red}{10} x& = & 47 \\\Leftrightarrow & x = \frac{47}{10} & & \\ & V = \left\{ \frac{47}{10} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 4x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 4x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{32}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{32x} +28 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{-32x} & = & \color{red}{32x} +28 \color{blue}{-32x} \color{blue}{+21} \\\Leftrightarrow & -280x-32x& = & 28+21 \\\Leftrightarrow & \color{red}{-312} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-312} & & \\\Leftrightarrow & x = \frac{-49}{312} & & \\ & V = \left\{ \frac{-49}{312} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-378}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -378x \color{red}{-90} & = & \color{red}{-105x} +35 \\\Leftrightarrow & -378x \color{red}{-90} \color{blue}{+90} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{+90} \\\Leftrightarrow & -378x+105x& = & 35+90 \\\Leftrightarrow & \color{red}{-273} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-273} & & \\\Leftrightarrow & x = \frac{-125}{273} & & \\ & V = \left\{ \frac{-125}{273} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{5}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{15}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-45} & = & \color{red}{-165x} +110 \\\Leftrightarrow & 198x \color{red}{-45} \color{blue}{+45} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+45} \\\Leftrightarrow & 198x+165x& = & 110+45 \\\Leftrightarrow & \color{red}{363} x& = & 155 \\\Leftrightarrow & x = \frac{155}{363} & & \\ & V = \left\{ \frac{155}{363} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x- \frac{128}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{-128} & = & \color{red}{-280x} +63 \\\Leftrightarrow & -672x \color{red}{-128} \color{blue}{+128} \color{blue}{+280x} & = & \color{red}{-280x} +63 \color{blue}{+280x} \color{blue}{+128} \\\Leftrightarrow & -672x+280x& = & 63+128 \\\Leftrightarrow & \color{red}{-392} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-392} & & \\\Leftrightarrow & x = \frac{-191}{392} & & \\ & V = \left\{ \frac{-191}{392} \right\} & \\\end{align}\)
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