Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{7})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-50} & = & \color{red}{245x} +28 \\\Leftrightarrow & -700x \color{red}{-50} \color{blue}{+50} \color{blue}{-245x} & = & \color{red}{245x} +28 \color{blue}{-245x} \color{blue}{+50} \\\Leftrightarrow & -700x-245x& = & 28+50 \\\Leftrightarrow & \color{red}{-945} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-945} & & \\\Leftrightarrow & x = \frac{-26}{315} & & \\ & V = \left\{ \frac{-26}{315} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{-15} & = & \color{red}{12x} +6 \\\Leftrightarrow & 100x \color{red}{-15} \color{blue}{+15} \color{blue}{-12x} & = & \color{red}{12x} +6 \color{blue}{-12x} \color{blue}{+15} \\\Leftrightarrow & 100x-12x& = & 6+15 \\\Leftrightarrow & \color{red}{88} x& = & 21 \\\Leftrightarrow & x = \frac{21}{88} & & \\ & V = \left\{ \frac{21}{88} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{2})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -14x+\frac{35}{2}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-196}{ \color{blue}{14} }x+ \frac{245}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{8}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -196x \color{red}{+245} & = & \color{red}{70x} +8 \\\Leftrightarrow & -196x \color{red}{+245} \color{blue}{-245} \color{blue}{-70x} & = & \color{red}{70x} +8 \color{blue}{-70x} \color{blue}{-245} \\\Leftrightarrow & -196x-70x& = & 8-245 \\\Leftrightarrow & \color{red}{-266} x& = & -237 \\\Leftrightarrow & x = \frac{-237}{-266} & & \\\Leftrightarrow & x = \frac{237}{266} & & \\ & V = \left\{ \frac{237}{266} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -10x+\frac{4}{11}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{+20} & = & \color{red}{385x} +22 \\\Leftrightarrow & -550x \color{red}{+20} \color{blue}{-20} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-20} \\\Leftrightarrow & -550x-385x& = & 22-20 \\\Leftrightarrow & \color{red}{-935} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-935} & & \\\Leftrightarrow & x = \frac{-2}{935} & & \\ & V = \left\{ \frac{-2}{935} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{9})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{8}{9}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{+40} & = & \color{red}{315x} +54 \\\Leftrightarrow & 720x \color{red}{+40} \color{blue}{-40} \color{blue}{-315x} & = & \color{red}{315x} +54 \color{blue}{-315x} \color{blue}{-40} \\\Leftrightarrow & 720x-315x& = & 54-40 \\\Leftrightarrow & \color{red}{405} x& = & 14 \\\Leftrightarrow & x = \frac{14}{405} & & \\ & V = \left\{ \frac{14}{405} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{5})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x+\frac{6}{5}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-360}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -360x \color{red}{+54} & = & \color{red}{405x} +50 \\\Leftrightarrow & -360x \color{red}{+54} \color{blue}{-54} \color{blue}{-405x} & = & \color{red}{405x} +50 \color{blue}{-405x} \color{blue}{-54} \\\Leftrightarrow & -360x-405x& = & 50-54 \\\Leftrightarrow & \color{red}{-765} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-765} & & \\\Leftrightarrow & x = \frac{4}{765} & & \\ & V = \left\{ \frac{4}{765} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x+\frac{20}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{20}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+20} & = & \color{red}{55x} +7 \\\Leftrightarrow & -132x \color{red}{+20} \color{blue}{-20} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{-20} \\\Leftrightarrow & -132x-55x& = & 7-20 \\\Leftrightarrow & \color{red}{-187} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-187} & & \\\Leftrightarrow & x = \frac{13}{187} & & \\ & V = \left\{ \frac{13}{187} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & 9x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{6}{11}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{-18} & = & \color{red}{297x} +88 \\\Leftrightarrow & -264x \color{red}{-18} \color{blue}{+18} \color{blue}{-297x} & = & \color{red}{297x} +88 \color{blue}{-297x} \color{blue}{+18} \\\Leftrightarrow & -264x-297x& = & 88+18 \\\Leftrightarrow & \color{red}{-561} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-561} & & \\\Leftrightarrow & x = \frac{-106}{561} & & \\ & V = \left\{ \frac{-106}{561} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{11})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -4x-\frac{10}{11}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-440}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{990}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -440x \color{red}{-100} & = & \color{red}{990x} +33 \\\Leftrightarrow & -440x \color{red}{-100} \color{blue}{+100} \color{blue}{-990x} & = & \color{red}{990x} +33 \color{blue}{-990x} \color{blue}{+100} \\\Leftrightarrow & -440x-990x& = & 33+100 \\\Leftrightarrow & \color{red}{-1430} x& = & 133 \\\Leftrightarrow & x = \frac{133}{-1430} & & \\\Leftrightarrow & x = \frac{-133}{1430} & & \\ & V = \left\{ \frac{-133}{1430} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{3}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 15-84 \\\Leftrightarrow & \color{red}{-595} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-595} & & \\\Leftrightarrow & x = \frac{69}{595} & & \\ & V = \left\{ \frac{69}{595} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{+36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 264x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & 264x+110x& = & 33-36 \\\Leftrightarrow & \color{red}{374} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{374} & & \\ & V = \left\{ \frac{-3}{374} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+88} & = & \color{red}{231x} +6 \\\Leftrightarrow & -528x \color{red}{+88} \color{blue}{-88} \color{blue}{-231x} & = & \color{red}{231x} +6 \color{blue}{-231x} \color{blue}{-88} \\\Leftrightarrow & -528x-231x& = & 6-88 \\\Leftrightarrow & \color{red}{-759} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-759} & & \\\Leftrightarrow & x = \frac{82}{759} & & \\ & V = \left\{ \frac{82}{759} \right\} & \\\end{align}\)
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