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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{-20} & = & \color{red}{-15x} +5 \\\Leftrightarrow & -36x \color{red}{-20} \color{blue}{+20} \color{blue}{+15x} & = & \color{red}{-15x} +5 \color{blue}{+15x} \color{blue}{+20} \\\Leftrightarrow & -36x+15x& = & 5+20 \\\Leftrightarrow & \color{red}{-21} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-21} & & \\\Leftrightarrow & x = \frac{-25}{21} & & \\ & V = \left\{ \frac{-25}{21} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{9}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+27} & = & \color{red}{105x} +56 \\\Leftrightarrow & -252x \color{red}{+27} \color{blue}{-27} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{-27} \\\Leftrightarrow & -252x-105x& = & 56-27 \\\Leftrightarrow & \color{red}{-357} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-357} & & \\\Leftrightarrow & x = \frac{-29}{357} & & \\ & V = \left\{ \frac{-29}{357} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -24x+\frac{30}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+330} & = & \color{red}{-385x} +28 \\\Leftrightarrow & -1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -1848x+385x& = & 28-330 \\\Leftrightarrow & \color{red}{-1463} x& = & -302 \\\Leftrightarrow & x = \frac{-302}{-1463} & & \\\Leftrightarrow & x = \frac{302}{1463} & & \\ & V = \left\{ \frac{302}{1463} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{7})& = & 4x+\frac{5}{11} \\\Leftrightarrow & -15x-\frac{20}{7}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{-220} & = & \color{red}{308x} +35 \\\Leftrightarrow & -1155x \color{red}{-220} \color{blue}{+220} \color{blue}{-308x} & = & \color{red}{308x} +35 \color{blue}{-308x} \color{blue}{+220} \\\Leftrightarrow & -1155x-308x& = & 35+220 \\\Leftrightarrow & \color{red}{-1463} x& = & 255 \\\Leftrightarrow & x = \frac{255}{-1463} & & \\\Leftrightarrow & x = \frac{-255}{1463} & & \\ & V = \left\{ \frac{-255}{1463} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -4x+\frac{9}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{9}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{36}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{-176x} +36 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +36 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & -660x+176x& = & 36-165 \\\Leftrightarrow & \color{red}{-484} x& = & -129 \\\Leftrightarrow & x = \frac{-129}{-484} & & \\\Leftrightarrow & x = \frac{129}{484} & & \\ & V = \left\{ \frac{129}{484} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{3}{8})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{21}{8}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{336}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 336x \color{red}{-63} & = & \color{red}{216x} +16 \\\Leftrightarrow & 336x \color{red}{-63} \color{blue}{+63} \color{blue}{-216x} & = & \color{red}{216x} +16 \color{blue}{-216x} \color{blue}{+63} \\\Leftrightarrow & 336x-216x& = & 16+63 \\\Leftrightarrow & \color{red}{120} x& = & 79 \\\Leftrightarrow & x = \frac{79}{120} & & \\ & V = \left\{ \frac{79}{120} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{8})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -9x+\frac{9}{8}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{+99} & = & \color{red}{440x} +64 \\\Leftrightarrow & -792x \color{red}{+99} \color{blue}{-99} \color{blue}{-440x} & = & \color{red}{440x} +64 \color{blue}{-440x} \color{blue}{-99} \\\Leftrightarrow & -792x-440x& = & 64-99 \\\Leftrightarrow & \color{red}{-1232} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-1232} & & \\\Leftrightarrow & x = \frac{5}{176} & & \\ & V = \left\{ \frac{5}{176} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-99x} +22 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{+30} \\\Leftrightarrow & 330x+99x& = & 22+30 \\\Leftrightarrow & \color{red}{429} x& = & 52 \\\Leftrightarrow & x = \frac{52}{429} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{2})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -15x+\frac{15}{2}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+45} & = & \color{red}{-48x} +4 \\\Leftrightarrow & -90x \color{red}{+45} \color{blue}{-45} \color{blue}{+48x} & = & \color{red}{-48x} +4 \color{blue}{+48x} \color{blue}{-45} \\\Leftrightarrow & -90x+48x& = & 4-45 \\\Leftrightarrow & \color{red}{-42} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-42} & & \\\Leftrightarrow & x = \frac{41}{42} & & \\ & V = \left\{ \frac{41}{42} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+40} & = & \color{red}{315x} +54 \\\Leftrightarrow & -270x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & -270x-315x& = & 54-40 \\\Leftrightarrow & \color{red}{-585} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-585} & & \\\Leftrightarrow & x = \frac{-14}{585} & & \\ & V = \left\{ \frac{-14}{585} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{5}{3})& = & 9x+\frac{4}{7} \\\Leftrightarrow & 8x-\frac{10}{3}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-70} & = & \color{red}{189x} +12 \\\Leftrightarrow & 168x \color{red}{-70} \color{blue}{+70} \color{blue}{-189x} & = & \color{red}{189x} +12 \color{blue}{-189x} \color{blue}{+70} \\\Leftrightarrow & 168x-189x& = & 12+70 \\\Leftrightarrow & \color{red}{-21} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-21} & & \\\Leftrightarrow & x = \frac{-82}{21} & & \\ & V = \left\{ \frac{-82}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{11})& = & -8x+\frac{4}{5} \\\Leftrightarrow & 21x+\frac{21}{11}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x+ \frac{105}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{-440x} +44 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{+440x} & = & \color{red}{-440x} +44 \color{blue}{+440x} \color{blue}{-105} \\\Leftrightarrow & 1155x+440x& = & 44-105 \\\Leftrightarrow & \color{red}{1595} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{1595} & & \\ & V = \left\{ \frac{-61}{1595} \right\} & \\\end{align}\)
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