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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-63x} +30 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{-140} \\\Leftrightarrow & 420x+63x& = & 30-140 \\\Leftrightarrow & \color{red}{483} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{483} & & \\ & V = \left\{ \frac{-110}{483} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{16}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-16} & = & \color{red}{15x} +4 \\\Leftrightarrow & 36x \color{red}{-16} \color{blue}{+16} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+16} \\\Leftrightarrow & 36x-15x& = & 4+16 \\\Leftrightarrow & \color{red}{21} x& = & 20 \\\Leftrightarrow & x = \frac{20}{21} & & \\ & V = \left\{ \frac{20}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{9})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -20x-\frac{16}{9}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{32}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-32} & = & \color{red}{162x} +63 \\\Leftrightarrow & -360x \color{red}{-32} \color{blue}{+32} \color{blue}{-162x} & = & \color{red}{162x} +63 \color{blue}{-162x} \color{blue}{+32} \\\Leftrightarrow & -360x-162x& = & 63+32 \\\Leftrightarrow & \color{red}{-522} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-522} & & \\\Leftrightarrow & x = \frac{-95}{522} & & \\ & V = \left\{ \frac{-95}{522} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & 330x+231x& = & 22+30 \\\Leftrightarrow & \color{red}{561} x& = & 52 \\\Leftrightarrow & x = \frac{52}{561} & & \\ & V = \left\{ \frac{52}{561} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & -7x+\frac{9}{8} \\\Leftrightarrow & 30x+\frac{24}{5}& = & -7x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1200}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1200x \color{red}{+192} & = & \color{red}{-280x} +45 \\\Leftrightarrow & 1200x \color{red}{+192} \color{blue}{-192} \color{blue}{+280x} & = & \color{red}{-280x} +45 \color{blue}{+280x} \color{blue}{-192} \\\Leftrightarrow & 1200x+280x& = & 45-192 \\\Leftrightarrow & \color{red}{1480} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{1480} & & \\ & V = \left\{ \frac{-147}{1480} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{8})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -20x-\frac{15}{8}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1120}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1120x \color{red}{-105} & = & \color{red}{-392x} +24 \\\Leftrightarrow & -1120x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +24 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & -1120x+392x& = & 24+105 \\\Leftrightarrow & \color{red}{-728} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-728} & & \\\Leftrightarrow & x = \frac{-129}{728} & & \\ & V = \left\{ \frac{-129}{728} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{5})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x-\frac{24}{5}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-216} & = & \color{red}{-315x} +10 \\\Leftrightarrow & -1350x \color{red}{-216} \color{blue}{+216} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{+216} \\\Leftrightarrow & -1350x+315x& = & 10+216 \\\Leftrightarrow & \color{red}{-1035} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-1035} & & \\\Leftrightarrow & x = \frac{-226}{1035} & & \\ & V = \left\{ \frac{-226}{1035} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-75} & = & \color{red}{385x} +44 \\\Leftrightarrow & 825x \color{red}{-75} \color{blue}{+75} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+75} \\\Leftrightarrow & 825x-385x& = & 44+75 \\\Leftrightarrow & \color{red}{440} x& = & 119 \\\Leftrightarrow & x = \frac{119}{440} & & \\ & V = \left\{ \frac{119}{440} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{4})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{16}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-135} & = & \color{red}{252x} +16 \\\Leftrightarrow & 720x \color{red}{-135} \color{blue}{+135} \color{blue}{-252x} & = & \color{red}{252x} +16 \color{blue}{-252x} \color{blue}{+135} \\\Leftrightarrow & 720x-252x& = & 16+135 \\\Leftrightarrow & \color{red}{468} x& = & 151 \\\Leftrightarrow & x = \frac{151}{468} & & \\ & V = \left\{ \frac{151}{468} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{5})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 21x-\frac{14}{5}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{945}{ \color{blue}{45} }x- \frac{126}{ \color{blue}{45} })& = & (\frac{90}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 945x \color{red}{-126} & = & \color{red}{90x} +50 \\\Leftrightarrow & 945x \color{red}{-126} \color{blue}{+126} \color{blue}{-90x} & = & \color{red}{90x} +50 \color{blue}{-90x} \color{blue}{+126} \\\Leftrightarrow & 945x-90x& = & 50+126 \\\Leftrightarrow & \color{red}{855} x& = & 176 \\\Leftrightarrow & x = \frac{176}{855} & & \\ & V = \left\{ \frac{176}{855} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{7})& = & -4x+\frac{3}{7} \\\Leftrightarrow & -15x+\frac{20}{7}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{20}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+20} & = & \color{red}{-28x} +3 \\\Leftrightarrow & -105x \color{red}{+20} \color{blue}{-20} \color{blue}{+28x} & = & \color{red}{-28x} +3 \color{blue}{+28x} \color{blue}{-20} \\\Leftrightarrow & -105x+28x& = & 3-20 \\\Leftrightarrow & \color{red}{-77} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-77} & & \\\Leftrightarrow & x = \frac{17}{77} & & \\ & V = \left\{ \frac{17}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-420}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{-90x} +21 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{+140} \\\Leftrightarrow & -420x+90x& = & 21+140 \\\Leftrightarrow & \color{red}{-330} x& = & 161 \\\Leftrightarrow & x = \frac{161}{-330} & & \\\Leftrightarrow & x = \frac{-161}{330} & & \\ & V = \left\{ \frac{-161}{330} \right\} & \\\end{align}\)
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