Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 35x+4& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{175}{ \color{blue}{5} }x+ \frac{20}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 175x \color{red}{+20} & = & \color{red}{15x} +6 \\\Leftrightarrow & 175x \color{red}{+20} \color{blue}{-20} \color{blue}{-15x} & = & \color{red}{15x} +6 \color{blue}{-15x} \color{blue}{-20} \\\Leftrightarrow & 175x-15x& = & 6-20 \\\Leftrightarrow & \color{red}{160} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{160} & & \\\Leftrightarrow & x = \frac{-7}{80} & & \\ & V = \left\{ \frac{-7}{80} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{3})& = & -9x+\frac{5}{6} \\\Leftrightarrow & -4x-\frac{4}{3}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-24}{ \color{blue}{6} }x- \frac{8}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -24x \color{red}{-8} & = & \color{red}{-54x} +5 \\\Leftrightarrow & -24x \color{red}{-8} \color{blue}{+8} \color{blue}{+54x} & = & \color{red}{-54x} +5 \color{blue}{+54x} \color{blue}{+8} \\\Leftrightarrow & -24x+54x& = & 5+8 \\\Leftrightarrow & \color{red}{30} x& = & 13 \\\Leftrightarrow & x = \frac{13}{30} & & \\ & V = \left\{ \frac{13}{30} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{9})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x- \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{-88} & = & \color{red}{-693x} +45 \\\Leftrightarrow & -594x \color{red}{-88} \color{blue}{+88} \color{blue}{+693x} & = & \color{red}{-693x} +45 \color{blue}{+693x} \color{blue}{+88} \\\Leftrightarrow & -594x+693x& = & 45+88 \\\Leftrightarrow & \color{red}{99} x& = & 133 \\\Leftrightarrow & x = \frac{133}{99} & & \\ & V = \left\{ \frac{133}{99} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & 7x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{30}{11}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-30} & = & \color{red}{77x} +7 \\\Leftrightarrow & 132x \color{red}{-30} \color{blue}{+30} \color{blue}{-77x} & = & \color{red}{77x} +7 \color{blue}{-77x} \color{blue}{+30} \\\Leftrightarrow & 132x-77x& = & 7+30 \\\Leftrightarrow & \color{red}{55} x& = & 37 \\\Leftrightarrow & x = \frac{37}{55} & & \\ & V = \left\{ \frac{37}{55} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 28x+\frac{14}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x+ \frac{14}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{+14} & = & \color{red}{-55x} +10 \\\Leftrightarrow & 308x \color{red}{+14} \color{blue}{-14} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{-14} \\\Leftrightarrow & 308x+55x& = & 10-14 \\\Leftrightarrow & \color{red}{363} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{363} & & \\ & V = \left\{ \frac{-4}{363} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{11})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 35x-\frac{21}{11}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{189}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-189} & = & \color{red}{198x} +110 \\\Leftrightarrow & 3465x \color{red}{-189} \color{blue}{+189} \color{blue}{-198x} & = & \color{red}{198x} +110 \color{blue}{-198x} \color{blue}{+189} \\\Leftrightarrow & 3465x-198x& = & 110+189 \\\Leftrightarrow & \color{red}{3267} x& = & 299 \\\Leftrightarrow & x = \frac{299}{3267} & & \\ & V = \left\{ \frac{299}{3267} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{7})& = & -4x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{20}{7}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+220} & = & \color{red}{-308x} +14 \\\Leftrightarrow & 1155x \color{red}{+220} \color{blue}{-220} \color{blue}{+308x} & = & \color{red}{-308x} +14 \color{blue}{+308x} \color{blue}{-220} \\\Leftrightarrow & 1155x+308x& = & 14-220 \\\Leftrightarrow & \color{red}{1463} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{1463} & & \\ & V = \left\{ \frac{-206}{1463} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{5}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{+150} \\\Leftrightarrow & 630x+175x& = & 56+150 \\\Leftrightarrow & \color{red}{805} x& = & 206 \\\Leftrightarrow & x = \frac{206}{805} & & \\ & V = \left\{ \frac{206}{805} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & -3x+\frac{7}{5} \\\Leftrightarrow & 14x+\frac{21}{8}& = & -3x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{560}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 560x \color{red}{+105} & = & \color{red}{-120x} +56 \\\Leftrightarrow & 560x \color{red}{+105} \color{blue}{-105} \color{blue}{+120x} & = & \color{red}{-120x} +56 \color{blue}{+120x} \color{blue}{-105} \\\Leftrightarrow & 560x+120x& = & 56-105 \\\Leftrightarrow & \color{red}{680} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{680} & & \\ & V = \left\{ \frac{-49}{680} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -18x+\frac{24}{5}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{45x} +9 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-45x} & = & \color{red}{45x} +9 \color{blue}{-45x} \color{blue}{-24} \\\Leftrightarrow & -90x-45x& = & 9-24 \\\Leftrightarrow & \color{red}{-135} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-135} & & \\\Leftrightarrow & x = \frac{1}{9} & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x+\frac{16}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{+112} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -1232x \color{red}{+112} \color{blue}{-112} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-112} \\\Leftrightarrow & -1232x+539x& = & 110-112 \\\Leftrightarrow & \color{red}{-693} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-693} & & \\\Leftrightarrow & x = \frac{2}{693} & & \\ & V = \left\{ \frac{2}{693} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{12})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 20x-\frac{25}{12}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 12 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{720}{ \color{blue}{36} }x- \frac{75}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 720x \color{red}{-75} & = & \color{red}{252x} +32 \\\Leftrightarrow & 720x \color{red}{-75} \color{blue}{+75} \color{blue}{-252x} & = & \color{red}{252x} +32 \color{blue}{-252x} \color{blue}{+75} \\\Leftrightarrow & 720x-252x& = & 32+75 \\\Leftrightarrow & \color{red}{468} x& = & 107 \\\Leftrightarrow & x = \frac{107}{468} & & \\ & V = \left\{ \frac{107}{468} \right\} & \\\end{align}\)
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