Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-70} & = & \color{red}{693x} +66 \\\Leftrightarrow & 616x \color{red}{-70} \color{blue}{+70} \color{blue}{-693x} & = & \color{red}{693x} +66 \color{blue}{-693x} \color{blue}{+70} \\\Leftrightarrow & 616x-693x& = & 66+70 \\\Leftrightarrow & \color{red}{-77} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-77} & & \\\Leftrightarrow & x = \frac{-136}{77} & & \\ & V = \left\{ \frac{-136}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & -7x+\frac{9}{11} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+66} & = & \color{red}{-385x} +45 \\\Leftrightarrow & 330x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +45 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & 330x+385x& = & 45-66 \\\Leftrightarrow & \color{red}{715} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{715} & & \\ & V = \left\{ \frac{-21}{715} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & 9x+\frac{3}{7} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 9x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{+147} & = & \color{red}{504x} +24 \\\Leftrightarrow & -1960x \color{red}{+147} \color{blue}{-147} \color{blue}{-504x} & = & \color{red}{504x} +24 \color{blue}{-504x} \color{blue}{-147} \\\Leftrightarrow & -1960x-504x& = & 24-147 \\\Leftrightarrow & \color{red}{-2464} x& = & -123 \\\Leftrightarrow & x = \frac{-123}{-2464} & & \\\Leftrightarrow & x = \frac{123}{2464} & & \\ & V = \left\{ \frac{123}{2464} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{2}{5})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{6}{5}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-50x} +15 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{+12} \\\Leftrightarrow & 60x+50x& = & 15+12 \\\Leftrightarrow & \color{red}{110} x& = & 27 \\\Leftrightarrow & x = \frac{27}{110} & & \\ & V = \left\{ \frac{27}{110} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{5})& = & -4x+\frac{3}{2} \\\Leftrightarrow & 21x-\frac{14}{5}& = & -4x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-40x} +15 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+40x} & = & \color{red}{-40x} +15 \color{blue}{+40x} \color{blue}{+28} \\\Leftrightarrow & 210x+40x& = & 15+28 \\\Leftrightarrow & \color{red}{250} x& = & 43 \\\Leftrightarrow & x = \frac{43}{250} & & \\ & V = \left\{ \frac{43}{250} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+90} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -252x \color{red}{+90} \color{blue}{-90} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-90} \\\Leftrightarrow & -252x+105x& = & 28-90 \\\Leftrightarrow & \color{red}{-147} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-147} & & \\\Leftrightarrow & x = \frac{62}{147} & & \\ & V = \left\{ \frac{62}{147} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{9})& = & 9x+\frac{9}{5} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{100}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+100} & = & \color{red}{405x} +81 \\\Leftrightarrow & 900x \color{red}{+100} \color{blue}{-100} \color{blue}{-405x} & = & \color{red}{405x} +81 \color{blue}{-405x} \color{blue}{-100} \\\Leftrightarrow & 900x-405x& = & 81-100 \\\Leftrightarrow & \color{red}{495} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{495} & & \\ & V = \left\{ \frac{-19}{495} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{3})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{231x} +12 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +12 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 660x-231x& = & 12-220 \\\Leftrightarrow & \color{red}{429} x& = & -208 \\\Leftrightarrow & x = \frac{-208}{429} & & \\\Leftrightarrow & x = \frac{-16}{33} & & \\ & V = \left\{ \frac{-16}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{7})& = & -9x+\frac{7}{6} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x+ \frac{96}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{+96} & = & \color{red}{-378x} +49 \\\Leftrightarrow & 840x \color{red}{+96} \color{blue}{-96} \color{blue}{+378x} & = & \color{red}{-378x} +49 \color{blue}{+378x} \color{blue}{-96} \\\Leftrightarrow & 840x+378x& = & 49-96 \\\Leftrightarrow & \color{red}{1218} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{1218} & & \\ & V = \left\{ \frac{-47}{1218} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 90x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{115} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{115} & & \\ & V = \left\{ \frac{-6}{115} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{11})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 25x-\frac{10}{11}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-70} & = & \color{red}{-154x} +99 \\\Leftrightarrow & 1925x \color{red}{-70} \color{blue}{+70} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+70} \\\Leftrightarrow & 1925x+154x& = & 99+70 \\\Leftrightarrow & \color{red}{2079} x& = & 169 \\\Leftrightarrow & x = \frac{169}{2079} & & \\ & V = \left\{ \frac{169}{2079} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{8})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 9x+\frac{15}{8}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{216}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{48}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 216x \color{red}{+45} & = & \color{red}{48x} +32 \\\Leftrightarrow & 216x \color{red}{+45} \color{blue}{-45} \color{blue}{-48x} & = & \color{red}{48x} +32 \color{blue}{-48x} \color{blue}{-45} \\\Leftrightarrow & 216x-48x& = & 32-45 \\\Leftrightarrow & \color{red}{168} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{168} & & \\ & V = \left\{ \frac{-13}{168} \right\} & \\\end{align}\)
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