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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{11})& = & -7x+\frac{4}{7} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+210} & = & \color{red}{-539x} +44 \\\Leftrightarrow & 2310x \color{red}{+210} \color{blue}{-210} \color{blue}{+539x} & = & \color{red}{-539x} +44 \color{blue}{+539x} \color{blue}{-210} \\\Leftrightarrow & 2310x+539x& = & 44-210 \\\Leftrightarrow & \color{red}{2849} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{2849} & & \\ & V = \left\{ \frac{-166}{2849} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{6}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-6} & = & \color{red}{-15x} +6 \\\Leftrightarrow & 20x \color{red}{-6} \color{blue}{+6} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{+6} \\\Leftrightarrow & 20x+15x& = & 6+6 \\\Leftrightarrow & \color{red}{35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{35} & & \\ & V = \left\{ \frac{12}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-32} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -168x \color{red}{-32} \color{blue}{+32} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+32} \\\Leftrightarrow & -168x+70x& = & 35+32 \\\Leftrightarrow & \color{red}{-98} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-98} & & \\\Leftrightarrow & x = \frac{-67}{98} & & \\ & V = \left\{ \frac{-67}{98} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+1)& = & 7x+\frac{9}{2} \\\Leftrightarrow & -10x-5& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-20}{ \color{blue}{2} }x- \frac{10}{ \color{blue}{2} })& = & (\frac{14}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -20x \color{red}{-10} & = & \color{red}{14x} +9 \\\Leftrightarrow & -20x \color{red}{-10} \color{blue}{+10} \color{blue}{-14x} & = & \color{red}{14x} +9 \color{blue}{-14x} \color{blue}{+10} \\\Leftrightarrow & -20x-14x& = & 9+10 \\\Leftrightarrow & \color{red}{-34} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-34} & & \\\Leftrightarrow & x = \frac{-19}{34} & & \\ & V = \left\{ \frac{-19}{34} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-32}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{+15} & = & \color{red}{-32x} +6 \\\Leftrightarrow & -60x \color{red}{+15} \color{blue}{-15} \color{blue}{+32x} & = & \color{red}{-32x} +6 \color{blue}{+32x} \color{blue}{-15} \\\Leftrightarrow & -60x+32x& = & 6-15 \\\Leftrightarrow & \color{red}{-28} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-28} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -2x+\frac{7}{10} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -2x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+24} & = & \color{red}{-20x} +7 \\\Leftrightarrow & 150x \color{red}{+24} \color{blue}{-24} \color{blue}{+20x} & = & \color{red}{-20x} +7 \color{blue}{+20x} \color{blue}{-24} \\\Leftrightarrow & 150x+20x& = & 7-24 \\\Leftrightarrow & \color{red}{170} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{170} & & \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{3}{4})& = & 4x+\frac{5}{2} \\\Leftrightarrow & 21x-\frac{21}{4}& = & 4x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{84}{ \color{blue}{4} }x- \frac{21}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 84x \color{red}{-21} & = & \color{red}{16x} +10 \\\Leftrightarrow & 84x \color{red}{-21} \color{blue}{+21} \color{blue}{-16x} & = & \color{red}{16x} +10 \color{blue}{-16x} \color{blue}{+21} \\\Leftrightarrow & 84x-16x& = & 10+21 \\\Leftrightarrow & \color{red}{68} x& = & 31 \\\Leftrightarrow & x = \frac{31}{68} & & \\ & V = \left\{ \frac{31}{68} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{7})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x+\frac{15}{7}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{45}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+45} & = & \color{red}{-105x} +35 \\\Leftrightarrow & -252x \color{red}{+45} \color{blue}{-45} \color{blue}{+105x} & = & \color{red}{-105x} +35 \color{blue}{+105x} \color{blue}{-45} \\\Leftrightarrow & -252x+105x& = & 35-45 \\\Leftrightarrow & \color{red}{-147} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-147} & & \\\Leftrightarrow & x = \frac{10}{147} & & \\ & V = \left\{ \frac{10}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-792}{ \color{blue}{66} }x- \frac{108}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -792x \color{red}{-108} & = & \color{red}{330x} +55 \\\Leftrightarrow & -792x \color{red}{-108} \color{blue}{+108} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{+108} \\\Leftrightarrow & -792x-330x& = & 55+108 \\\Leftrightarrow & \color{red}{-1122} x& = & 163 \\\Leftrightarrow & x = \frac{163}{-1122} & & \\\Leftrightarrow & x = \frac{-163}{1122} & & \\ & V = \left\{ \frac{-163}{1122} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{12}{11}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-60} & = & \color{red}{165x} +66 \\\Leftrightarrow & 440x \color{red}{-60} \color{blue}{+60} \color{blue}{-165x} & = & \color{red}{165x} +66 \color{blue}{-165x} \color{blue}{+60} \\\Leftrightarrow & 440x-165x& = & 66+60 \\\Leftrightarrow & \color{red}{275} x& = & 126 \\\Leftrightarrow & x = \frac{126}{275} & & \\ & V = \left\{ \frac{126}{275} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 4x+\frac{3}{2} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{56}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{+20} & = & \color{red}{56x} +21 \\\Leftrightarrow & -210x \color{red}{+20} \color{blue}{-20} \color{blue}{-56x} & = & \color{red}{56x} +21 \color{blue}{-56x} \color{blue}{-20} \\\Leftrightarrow & -210x-56x& = & 21-20 \\\Leftrightarrow & \color{red}{-266} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-266} & & \\\Leftrightarrow & x = \frac{-1}{266} & & \\ & V = \left\{ \frac{-1}{266} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{2})& = & -8x+\frac{2}{9} \\\Leftrightarrow & 21x+\frac{21}{2}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{378}{ \color{blue}{18} }x+ \frac{189}{ \color{blue}{18} })& = & (\frac{-144}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 378x \color{red}{+189} & = & \color{red}{-144x} +4 \\\Leftrightarrow & 378x \color{red}{+189} \color{blue}{-189} \color{blue}{+144x} & = & \color{red}{-144x} +4 \color{blue}{+144x} \color{blue}{-189} \\\Leftrightarrow & 378x+144x& = & 4-189 \\\Leftrightarrow & \color{red}{522} x& = & -185 \\\Leftrightarrow & x = \frac{-185}{522} & & \\ & V = \left\{ \frac{-185}{522} \right\} & \\\end{align}\)
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