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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-126} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & -924x-385x& = & 110+126 \\\Leftrightarrow & \color{red}{-1309} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-1309} & & \\\Leftrightarrow & x = \frac{-236}{1309} & & \\ & V = \left\{ \frac{-236}{1309} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+105} & = & \color{red}{-224x} +16 \\\Leftrightarrow & -420x \color{red}{+105} \color{blue}{-105} \color{blue}{+224x} & = & \color{red}{-224x} +16 \color{blue}{+224x} \color{blue}{-105} \\\Leftrightarrow & -420x+224x& = & 16-105 \\\Leftrightarrow & \color{red}{-196} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-196} & & \\\Leftrightarrow & x = \frac{89}{196} & & \\ & V = \left\{ \frac{89}{196} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{8})& = & 8x+\frac{10}{9} \\\Leftrightarrow & -21x-\frac{35}{8}& = & 8x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1512}{ \color{blue}{72} }x- \frac{315}{ \color{blue}{72} })& = & (\frac{576}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1512x \color{red}{-315} & = & \color{red}{576x} +80 \\\Leftrightarrow & -1512x \color{red}{-315} \color{blue}{+315} \color{blue}{-576x} & = & \color{red}{576x} +80 \color{blue}{-576x} \color{blue}{+315} \\\Leftrightarrow & -1512x-576x& = & 80+315 \\\Leftrightarrow & \color{red}{-2088} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-2088} & & \\\Leftrightarrow & x = \frac{-395}{2088} & & \\ & V = \left\{ \frac{-395}{2088} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -30x-\frac{24}{11}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-1980}{ \color{blue}{66} }x- \frac{144}{ \color{blue}{66} })& = & (\frac{-462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -1980x \color{red}{-144} & = & \color{red}{-462x} +55 \\\Leftrightarrow & -1980x \color{red}{-144} \color{blue}{+144} \color{blue}{+462x} & = & \color{red}{-462x} +55 \color{blue}{+462x} \color{blue}{+144} \\\Leftrightarrow & -1980x+462x& = & 55+144 \\\Leftrightarrow & \color{red}{-1518} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1518} & & \\\Leftrightarrow & x = \frac{-199}{1518} & & \\ & V = \left\{ \frac{-199}{1518} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{7})& = & 4x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+10} & = & \color{red}{28x} +8 \\\Leftrightarrow & -105x \color{red}{+10} \color{blue}{-10} \color{blue}{-28x} & = & \color{red}{28x} +8 \color{blue}{-28x} \color{blue}{-10} \\\Leftrightarrow & -105x-28x& = & 8-10 \\\Leftrightarrow & \color{red}{-133} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-133} & & \\\Leftrightarrow & x = \frac{2}{133} & & \\ & V = \left\{ \frac{2}{133} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+27} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -180x \color{red}{+27} \color{blue}{-27} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-27} \\\Leftrightarrow & -180x+75x& = & 40-27 \\\Leftrightarrow & \color{red}{-105} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-105} & & \\\Leftrightarrow & x = \frac{-13}{105} & & \\ & V = \left\{ \frac{-13}{105} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 28x+\frac{21}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x+ \frac{210}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{+210} & = & \color{red}{550x} +99 \\\Leftrightarrow & 3080x \color{red}{+210} \color{blue}{-210} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{-210} \\\Leftrightarrow & 3080x-550x& = & 99-210 \\\Leftrightarrow & \color{red}{2530} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{2530} & & \\ & V = \left\{ \frac{-111}{2530} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{231x} +44 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-30} \\\Leftrightarrow & -330x-231x& = & 44-30 \\\Leftrightarrow & \color{red}{-561} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-561} & & \\\Leftrightarrow & x = \frac{-14}{561} & & \\ & V = \left\{ \frac{-14}{561} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{-385x} +28 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{+385x} & = & \color{red}{-385x} +28 \color{blue}{+385x} \color{blue}{+330} \\\Leftrightarrow & 1848x+385x& = & 28+330 \\\Leftrightarrow & \color{red}{2233} x& = & 358 \\\Leftrightarrow & x = \frac{358}{2233} & & \\ & V = \left\{ \frac{358}{2233} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 8x+\frac{10}{7}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{224}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 224x \color{red}{+40} & = & \color{red}{-196x} +21 \\\Leftrightarrow & 224x \color{red}{+40} \color{blue}{-40} \color{blue}{+196x} & = & \color{red}{-196x} +21 \color{blue}{+196x} \color{blue}{-40} \\\Leftrightarrow & 224x+196x& = & 21-40 \\\Leftrightarrow & \color{red}{420} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{420} & & \\ & V = \left\{ \frac{-19}{420} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{11})& = & -5x+\frac{3}{7} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+70} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -1925x \color{red}{+70} \color{blue}{-70} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{-70} \\\Leftrightarrow & -1925x+385x& = & 33-70 \\\Leftrightarrow & \color{red}{-1540} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-1540} & & \\\Leftrightarrow & x = \frac{37}{1540} & & \\ & V = \left\{ \frac{37}{1540} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +25 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 25-84 \\\Leftrightarrow & \color{red}{-595} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-595} & & \\\Leftrightarrow & x = \frac{59}{595} & & \\ & V = \left\{ \frac{59}{595} \right\} & \\\end{align}\)
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