Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +30 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 30-132 \\\Leftrightarrow & \color{red}{-935} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-935} & & \\\Leftrightarrow & x = \frac{6}{55} & & \\ & V = \left\{ \frac{6}{55} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{4}{7})& = & 3x+\frac{8}{7} \\\Leftrightarrow & 25x-\frac{20}{7}& = & 3x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{175}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 175x \color{red}{-20} & = & \color{red}{21x} +8 \\\Leftrightarrow & 175x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 175x-21x& = & 8+20 \\\Leftrightarrow & \color{red}{154} x& = & 28 \\\Leftrightarrow & x = \frac{28}{154} & & \\\Leftrightarrow & x = \frac{2}{11} & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{12})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 14x+\frac{35}{12}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{+35} & = & \color{red}{36x} +16 \\\Leftrightarrow & 168x \color{red}{+35} \color{blue}{-35} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{-35} \\\Leftrightarrow & 168x-36x& = & 16-35 \\\Leftrightarrow & \color{red}{132} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{132} & & \\ & V = \left\{ \frac{-19}{132} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{539x} +56 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -770x-539x& = & 56-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{-1309} & & \\\Leftrightarrow & x = \frac{54}{1309} & & \\ & V = \left\{ \frac{54}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{11})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 28x-\frac{14}{11}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{112}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-112} & = & \color{red}{-792x} +77 \\\Leftrightarrow & 2464x \color{red}{-112} \color{blue}{+112} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+112} \\\Leftrightarrow & 2464x+792x& = & 77+112 \\\Leftrightarrow & \color{red}{3256} x& = & 189 \\\Leftrightarrow & x = \frac{189}{3256} & & \\ & V = \left\{ \frac{189}{3256} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{24}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+168} & = & \color{red}{-175x} +50 \\\Leftrightarrow & 420x \color{red}{+168} \color{blue}{-168} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{-168} \\\Leftrightarrow & 420x+175x& = & 50-168 \\\Leftrightarrow & \color{red}{595} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{595} & & \\ & V = \left\{ \frac{-118}{595} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-105x} +56 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-90} \\\Leftrightarrow & 252x+105x& = & 56-90 \\\Leftrightarrow & \color{red}{357} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{357} & & \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-126} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & 1848x+385x& = & 110+126 \\\Leftrightarrow & \color{red}{2233} x& = & 236 \\\Leftrightarrow & x = \frac{236}{2233} & & \\ & V = \left\{ \frac{236}{2233} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{2})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-165} & = & \color{red}{88x} +20 \\\Leftrightarrow & -330x \color{red}{-165} \color{blue}{+165} \color{blue}{-88x} & = & \color{red}{88x} +20 \color{blue}{-88x} \color{blue}{+165} \\\Leftrightarrow & -330x-88x& = & 20+165 \\\Leftrightarrow & \color{red}{-418} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-418} & & \\\Leftrightarrow & x = \frac{-185}{418} & & \\ & V = \left\{ \frac{-185}{418} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{-10} & = & \color{red}{-35x} +4 \\\Leftrightarrow & 28x \color{red}{-10} \color{blue}{+10} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+10} \\\Leftrightarrow & 28x+35x& = & 4+10 \\\Leftrightarrow & \color{red}{63} x& = & 14 \\\Leftrightarrow & x = \frac{14}{63} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -14x+\frac{35}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+385} & = & \color{red}{-297x} +54 \\\Leftrightarrow & -1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{-385} \\\Leftrightarrow & -1386x+297x& = & 54-385 \\\Leftrightarrow & \color{red}{-1089} x& = & -331 \\\Leftrightarrow & x = \frac{-331}{-1089} & & \\\Leftrightarrow & x = \frac{331}{1089} & & \\ & V = \left\{ \frac{331}{1089} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{3}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{6}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+18} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -90x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -90x+105x& = & 20-18 \\\Leftrightarrow & \color{red}{15} x& = & 2 \\\Leftrightarrow & x = \frac{2}{15} & & \\ & V = \left\{ \frac{2}{15} \right\} & \\\end{align}\)
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