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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{5})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -10x+\frac{8}{5}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-400}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -400x \color{red}{+64} & = & \color{red}{280x} +15 \\\Leftrightarrow & -400x \color{red}{+64} \color{blue}{-64} \color{blue}{-280x} & = & \color{red}{280x} +15 \color{blue}{-280x} \color{blue}{-64} \\\Leftrightarrow & -400x-280x& = & 15-64 \\\Leftrightarrow & \color{red}{-680} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-680} & & \\\Leftrightarrow & x = \frac{49}{680} & & \\ & V = \left\{ \frac{49}{680} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{360}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 360x \color{red}{-48} & = & \color{red}{100x} +45 \\\Leftrightarrow & 360x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & 360x-100x& = & 45+48 \\\Leftrightarrow & \color{red}{260} x& = & 93 \\\Leftrightarrow & x = \frac{93}{260} & & \\ & V = \left\{ \frac{93}{260} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-132} & = & \color{red}{-385x} +40 \\\Leftrightarrow & -1650x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +40 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1650x+385x& = & 40+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1265} & & \\\Leftrightarrow & x = \frac{-172}{1265} & & \\ & V = \left\{ \frac{-172}{1265} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -20x+\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & -1100x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & -1100x+385x& = & 50-132 \\\Leftrightarrow & \color{red}{-715} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-715} & & \\\Leftrightarrow & x = \frac{82}{715} & & \\ & V = \left\{ \frac{82}{715} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{3}{2})& = & 5x+\frac{7}{4} \\\Leftrightarrow & -9x+\frac{9}{2}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-36}{ \color{blue}{4} }x+ \frac{18}{ \color{blue}{4} })& = & (\frac{20}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -36x \color{red}{+18} & = & \color{red}{20x} +7 \\\Leftrightarrow & -36x \color{red}{+18} \color{blue}{-18} \color{blue}{-20x} & = & \color{red}{20x} +7 \color{blue}{-20x} \color{blue}{-18} \\\Leftrightarrow & -36x-20x& = & 7-18 \\\Leftrightarrow & \color{red}{-56} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-56} & & \\\Leftrightarrow & x = \frac{11}{56} & & \\ & V = \left\{ \frac{11}{56} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{-165x} +24 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +24 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 264x+165x& = & 24+88 \\\Leftrightarrow & \color{red}{429} x& = & 112 \\\Leftrightarrow & x = \frac{112}{429} & & \\ & V = \left\{ \frac{112}{429} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -9x-\frac{15}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-297}{ \color{blue}{33} }x- \frac{45}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -297x \color{red}{-45} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -297x \color{red}{-45} \color{blue}{+45} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+45} \\\Leftrightarrow & -297x+165x& = & 110+45 \\\Leftrightarrow & \color{red}{-132} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-132} & & \\\Leftrightarrow & x = \frac{-155}{132} & & \\ & V = \left\{ \frac{-155}{132} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-70x} +42 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{-30} \\\Leftrightarrow & 525x+70x& = & 42-30 \\\Leftrightarrow & \color{red}{595} x& = & 12 \\\Leftrightarrow & x = \frac{12}{595} & & \\ & V = \left\{ \frac{12}{595} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{63x} +14 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 210x-63x& = & 14-30 \\\Leftrightarrow & \color{red}{147} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{147} & & \\ & V = \left\{ \frac{-16}{147} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{-24} & = & \color{red}{70x} +25 \\\Leftrightarrow & 200x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 200x-70x& = & 25+24 \\\Leftrightarrow & \color{red}{130} x& = & 49 \\\Leftrightarrow & x = \frac{49}{130} & & \\ & V = \left\{ \frac{49}{130} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-60} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 264x \color{red}{-60} \color{blue}{+60} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{+60} \\\Leftrightarrow & 264x+154x& = & 33+60 \\\Leftrightarrow & \color{red}{418} x& = & 93 \\\Leftrightarrow & x = \frac{93}{418} & & \\ & V = \left\{ \frac{93}{418} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{5})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -12x-\frac{24}{5}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{96}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-96} & = & \color{red}{-100x} +35 \\\Leftrightarrow & -240x \color{red}{-96} \color{blue}{+96} \color{blue}{+100x} & = & \color{red}{-100x} +35 \color{blue}{+100x} \color{blue}{+96} \\\Leftrightarrow & -240x+100x& = & 35+96 \\\Leftrightarrow & \color{red}{-140} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-140} & & \\\Leftrightarrow & x = \frac{-131}{140} & & \\ & V = \left\{ \frac{-131}{140} \right\} & \\\end{align}\)
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