Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{7})& = & 3x+\frac{3}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{231x} +21 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +21 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 1540x-231x& = & 21-220 \\\Leftrightarrow & \color{red}{1309} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{1309} & & \\ & V = \left\{ \frac{-199}{1309} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{9}{4} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{100x} +45 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{-100x} & = & \color{red}{100x} +45 \color{blue}{-100x} \color{blue}{+48} \\\Leftrightarrow & -180x-100x& = & 45+48 \\\Leftrightarrow & \color{red}{-280} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-280} & & \\\Leftrightarrow & x = \frac{-93}{280} & & \\ & V = \left\{ \frac{-93}{280} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & 9x+\frac{7}{8} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-448}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -448x \color{red}{+80} & = & \color{red}{504x} +49 \\\Leftrightarrow & -448x \color{red}{+80} \color{blue}{-80} \color{blue}{-504x} & = & \color{red}{504x} +49 \color{blue}{-504x} \color{blue}{-80} \\\Leftrightarrow & -448x-504x& = & 49-80 \\\Leftrightarrow & \color{red}{-952} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-952} & & \\\Leftrightarrow & x = \frac{31}{952} & & \\ & V = \left\{ \frac{31}{952} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-6} & = & \color{red}{-20x} +9 \\\Leftrightarrow & -75x \color{red}{-6} \color{blue}{+6} \color{blue}{+20x} & = & \color{red}{-20x} +9 \color{blue}{+20x} \color{blue}{+6} \\\Leftrightarrow & -75x+20x& = & 9+6 \\\Leftrightarrow & \color{red}{-55} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-55} & & \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{11})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{10}{11}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1320}{ \color{blue}{132} }x+ \frac{120}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{-924x} +77 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+924x} & = & \color{red}{-924x} +77 \color{blue}{+924x} \color{blue}{-120} \\\Leftrightarrow & -1320x+924x& = & 77-120 \\\Leftrightarrow & \color{red}{-396} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-396} & & \\\Leftrightarrow & x = \frac{43}{396} & & \\ & V = \left\{ \frac{43}{396} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{3})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 4x+\frac{8}{3}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{+24} & = & \color{red}{63x} +10 \\\Leftrightarrow & 36x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 36x-63x& = & 10-24 \\\Leftrightarrow & \color{red}{-27} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-27} & & \\\Leftrightarrow & x = \frac{14}{27} & & \\ & V = \left\{ \frac{14}{27} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{7})& = & 5x+\frac{5}{8} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{35}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-240} & = & \color{red}{280x} +35 \\\Leftrightarrow & 672x \color{red}{-240} \color{blue}{+240} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{+240} \\\Leftrightarrow & 672x-280x& = & 35+240 \\\Leftrightarrow & \color{red}{392} x& = & 275 \\\Leftrightarrow & x = \frac{275}{392} & & \\ & V = \left\{ \frac{275}{392} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{210}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 210x \color{red}{+12} & = & \color{red}{-28x} +63 \\\Leftrightarrow & 210x \color{red}{+12} \color{blue}{-12} \color{blue}{+28x} & = & \color{red}{-28x} +63 \color{blue}{+28x} \color{blue}{-12} \\\Leftrightarrow & 210x+28x& = & 63-12 \\\Leftrightarrow & \color{red}{238} x& = & 51 \\\Leftrightarrow & x = \frac{51}{238} & & \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +10 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +10 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 10+132 \\\Leftrightarrow & \color{red}{-385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-385} & & \\\Leftrightarrow & x = \frac{-142}{385} & & \\ & V = \left\{ \frac{-142}{385} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 24x+\frac{30}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1584}{ \color{blue}{66} }x+ \frac{180}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1584x \color{red}{+180} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 1584x \color{red}{+180} \color{blue}{-180} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-180} \\\Leftrightarrow & 1584x+330x& = & 55-180 \\\Leftrightarrow & \color{red}{1914} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{1914} & & \\ & V = \left\{ \frac{-125}{1914} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-80} & = & \color{red}{24x} +9 \\\Leftrightarrow & 180x \color{red}{-80} \color{blue}{+80} \color{blue}{-24x} & = & \color{red}{24x} +9 \color{blue}{-24x} \color{blue}{+80} \\\Leftrightarrow & 180x-24x& = & 9+80 \\\Leftrightarrow & \color{red}{156} x& = & 89 \\\Leftrightarrow & x = \frac{89}{156} & & \\ & V = \left\{ \frac{89}{156} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & 4x+\frac{9}{4} \\\Leftrightarrow & -15x+\frac{9}{5}& = & 4x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{36}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+36} & = & \color{red}{80x} +45 \\\Leftrightarrow & -300x \color{red}{+36} \color{blue}{-36} \color{blue}{-80x} & = & \color{red}{80x} +45 \color{blue}{-80x} \color{blue}{-36} \\\Leftrightarrow & -300x-80x& = & 45-36 \\\Leftrightarrow & \color{red}{-380} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-380} & & \\\Leftrightarrow & x = \frac{-9}{380} & & \\ & V = \left\{ \frac{-9}{380} \right\} & \\\end{align}\)
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