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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{3}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 8x-\frac{6}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-30} & = & \color{red}{-385x} +33 \\\Leftrightarrow & 440x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & 440x+385x& = & 33+30 \\\Leftrightarrow & \color{red}{825} x& = & 63 \\\Leftrightarrow & x = \frac{63}{825} & & \\\Leftrightarrow & x = \frac{21}{275} & & \\ & V = \left\{ \frac{21}{275} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{2}{7})& = & 6x+\frac{2}{11} \\\Leftrightarrow & -25x-\frac{10}{7}& = & 6x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{-110} & = & \color{red}{462x} +14 \\\Leftrightarrow & -1925x \color{red}{-110} \color{blue}{+110} \color{blue}{-462x} & = & \color{red}{462x} +14 \color{blue}{-462x} \color{blue}{+110} \\\Leftrightarrow & -1925x-462x& = & 14+110 \\\Leftrightarrow & \color{red}{-2387} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-2387} & & \\\Leftrightarrow & x = \frac{-4}{77} & & \\ & V = \left\{ \frac{-4}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-6} & = & \color{red}{63x} +10 \\\Leftrightarrow & 70x \color{red}{-6} \color{blue}{+6} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{+6} \\\Leftrightarrow & 70x-63x& = & 10+6 \\\Leftrightarrow & \color{red}{7} x& = & 16 \\\Leftrightarrow & x = \frac{16}{7} & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{5}{8})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{25}{8}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1760}{ \color{blue}{88} }x- \frac{275}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1760x \color{red}{-275} & = & \color{red}{616x} +48 \\\Leftrightarrow & -1760x \color{red}{-275} \color{blue}{+275} \color{blue}{-616x} & = & \color{red}{616x} +48 \color{blue}{-616x} \color{blue}{+275} \\\Leftrightarrow & -1760x-616x& = & 48+275 \\\Leftrightarrow & \color{red}{-2376} x& = & 323 \\\Leftrightarrow & x = \frac{323}{-2376} & & \\\Leftrightarrow & x = \frac{-323}{2376} & & \\ & V = \left\{ \frac{-323}{2376} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{+54} & = & \color{red}{441x} +56 \\\Leftrightarrow & -378x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +56 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & -378x-441x& = & 56-54 \\\Leftrightarrow & \color{red}{-819} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-819} & & \\\Leftrightarrow & x = \frac{-2}{819} & & \\ & V = \left\{ \frac{-2}{819} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{11})& = & -7x+\frac{8}{11} \\\Leftrightarrow & 8x-\frac{20}{11}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{20}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-20} & = & \color{red}{-77x} +8 \\\Leftrightarrow & 88x \color{red}{-20} \color{blue}{+20} \color{blue}{+77x} & = & \color{red}{-77x} +8 \color{blue}{+77x} \color{blue}{+20} \\\Leftrightarrow & 88x+77x& = & 8+20 \\\Leftrightarrow & \color{red}{165} x& = & 28 \\\Leftrightarrow & x = \frac{28}{165} & & \\ & V = \left\{ \frac{28}{165} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{7})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -10x+\frac{25}{7}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{275}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+275} & = & \color{red}{-539x} +21 \\\Leftrightarrow & -770x \color{red}{+275} \color{blue}{-275} \color{blue}{+539x} & = & \color{red}{-539x} +21 \color{blue}{+539x} \color{blue}{-275} \\\Leftrightarrow & -770x+539x& = & 21-275 \\\Leftrightarrow & \color{red}{-231} x& = & -254 \\\Leftrightarrow & x = \frac{-254}{-231} & & \\\Leftrightarrow & x = \frac{254}{231} & & \\ & V = \left\{ \frac{254}{231} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{8}{9}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+8} & = & \color{red}{-63x} +12 \\\Leftrightarrow & -90x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +12 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & -90x+63x& = & 12-8 \\\Leftrightarrow & \color{red}{-27} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-27} & & \\\Leftrightarrow & x = \frac{-4}{27} & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-30} & = & \color{red}{-49x} +9 \\\Leftrightarrow & 84x \color{red}{-30} \color{blue}{+30} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+30} \\\Leftrightarrow & 84x+49x& = & 9+30 \\\Leftrightarrow & \color{red}{133} x& = & 39 \\\Leftrightarrow & x = \frac{39}{133} & & \\ & V = \left\{ \frac{39}{133} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{12})& = & 9x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{25}{12}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{1320}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{1188}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 1320x \color{red}{-275} & = & \color{red}{1188x} +72 \\\Leftrightarrow & 1320x \color{red}{-275} \color{blue}{+275} \color{blue}{-1188x} & = & \color{red}{1188x} +72 \color{blue}{-1188x} \color{blue}{+275} \\\Leftrightarrow & 1320x-1188x& = & 72+275 \\\Leftrightarrow & \color{red}{132} x& = & 347 \\\Leftrightarrow & x = \frac{347}{132} & & \\ & V = \left\{ \frac{347}{132} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{12}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-36} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -252x+105x& = & 56+36 \\\Leftrightarrow & \color{red}{-147} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-147} & & \\\Leftrightarrow & x = \frac{-92}{147} & & \\ & V = \left\{ \frac{-92}{147} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{5})& = & 6x+\frac{10}{9} \\\Leftrightarrow & -35x-\frac{14}{5}& = & 6x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1575}{ \color{blue}{45} }x- \frac{126}{ \color{blue}{45} })& = & (\frac{270}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1575x \color{red}{-126} & = & \color{red}{270x} +50 \\\Leftrightarrow & -1575x \color{red}{-126} \color{blue}{+126} \color{blue}{-270x} & = & \color{red}{270x} +50 \color{blue}{-270x} \color{blue}{+126} \\\Leftrightarrow & -1575x-270x& = & 50+126 \\\Leftrightarrow & \color{red}{-1845} x& = & 176 \\\Leftrightarrow & x = \frac{176}{-1845} & & \\\Leftrightarrow & x = \frac{-176}{1845} & & \\ & V = \left\{ \frac{-176}{1845} \right\} & \\\end{align}\)
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