Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{3})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{+220} & = & \color{red}{231x} +12 \\\Leftrightarrow & 660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +12 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 660x-231x& = & 12-220 \\\Leftrightarrow & \color{red}{429} x& = & -208 \\\Leftrightarrow & x = \frac{-208}{429} & & \\\Leftrightarrow & x = \frac{-16}{33} & & \\ & V = \left\{ \frac{-16}{33} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{24}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x+ \frac{120}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{+120} & = & \color{red}{315x} +42 \\\Leftrightarrow & -630x \color{red}{+120} \color{blue}{-120} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{-120} \\\Leftrightarrow & -630x-315x& = & 42-120 \\\Leftrightarrow & \color{red}{-945} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{-945} & & \\\Leftrightarrow & x = \frac{26}{315} & & \\ & V = \left\{ \frac{26}{315} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{8}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+24} & = & \color{red}{-99x} +22 \\\Leftrightarrow & -264x \color{red}{+24} \color{blue}{-24} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{-24} \\\Leftrightarrow & -264x+99x& = & 22-24 \\\Leftrightarrow & \color{red}{-165} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-165} & & \\\Leftrightarrow & x = \frac{2}{165} & & \\ & V = \left\{ \frac{2}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{-20} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -280x \color{red}{-20} \color{blue}{+20} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+20} \\\Leftrightarrow & -280x+98x& = & 21+20 \\\Leftrightarrow & \color{red}{-182} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-182} & & \\\Leftrightarrow & x = \frac{-41}{182} & & \\ & V = \left\{ \frac{-41}{182} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -270x+135x& = & 50+36 \\\Leftrightarrow & \color{red}{-135} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-135} & & \\\Leftrightarrow & x = \frac{-86}{135} & & \\ & V = \left\{ \frac{-86}{135} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{11})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -18x+\frac{24}{11}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+168} & = & \color{red}{693x} +99 \\\Leftrightarrow & -1386x \color{red}{+168} \color{blue}{-168} \color{blue}{-693x} & = & \color{red}{693x} +99 \color{blue}{-693x} \color{blue}{-168} \\\Leftrightarrow & -1386x-693x& = & 99-168 \\\Leftrightarrow & \color{red}{-2079} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-2079} & & \\\Leftrightarrow & x = \frac{23}{693} & & \\ & V = \left\{ \frac{23}{693} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 12x-\frac{24}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x- \frac{96}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{-96} & = & \color{red}{220x} +33 \\\Leftrightarrow & 528x \color{red}{-96} \color{blue}{+96} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{+96} \\\Leftrightarrow & 528x-220x& = & 33+96 \\\Leftrightarrow & \color{red}{308} x& = & 129 \\\Leftrightarrow & x = \frac{129}{308} & & \\ & V = \left\{ \frac{129}{308} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{7})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{175x} +28 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-175x} & = & \color{red}{175x} +28 \color{blue}{-175x} \color{blue}{+100} \\\Leftrightarrow & 560x-175x& = & 28+100 \\\Leftrightarrow & \color{red}{385} x& = & 128 \\\Leftrightarrow & x = \frac{128}{385} & & \\ & V = \left\{ \frac{128}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{1}{3})& = & -6x+\frac{10}{9} \\\Leftrightarrow & -35x-\frac{7}{3}& = & -6x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{21}{ \color{blue}{9} })& = & (\frac{-54}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-21} & = & \color{red}{-54x} +10 \\\Leftrightarrow & -315x \color{red}{-21} \color{blue}{+21} \color{blue}{+54x} & = & \color{red}{-54x} +10 \color{blue}{+54x} \color{blue}{+21} \\\Leftrightarrow & -315x+54x& = & 10+21 \\\Leftrightarrow & \color{red}{-261} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-261} & & \\\Leftrightarrow & x = \frac{-31}{261} & & \\ & V = \left\{ \frac{-31}{261} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{539x} +21 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{-220} \\\Leftrightarrow & 1540x-539x& = & 21-220 \\\Leftrightarrow & \color{red}{1001} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{1001} & & \\ & V = \left\{ \frac{-199}{1001} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{6})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 21x-\frac{35}{6}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-35} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 126x \color{red}{-35} \color{blue}{+35} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{+35} \\\Leftrightarrow & 126x+12x& = & 9+35 \\\Leftrightarrow & \color{red}{138} x& = & 44 \\\Leftrightarrow & x = \frac{44}{138} & & \\\Leftrightarrow & x = \frac{22}{69} & & \\ & V = \left\{ \frac{22}{69} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{-60} & = & \color{red}{-210x} +63 \\\Leftrightarrow & 280x \color{red}{-60} \color{blue}{+60} \color{blue}{+210x} & = & \color{red}{-210x} +63 \color{blue}{+210x} \color{blue}{+60} \\\Leftrightarrow & 280x+210x& = & 63+60 \\\Leftrightarrow & \color{red}{490} x& = & 123 \\\Leftrightarrow & x = \frac{123}{490} & & \\ & V = \left\{ \frac{123}{490} \right\} & \\\end{align}\)
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