Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & 270x-75x& = & 10+36 \\\Leftrightarrow & \color{red}{195} x& = & 46 \\\Leftrightarrow & x = \frac{46}{195} & & \\ & V = \left\{ \frac{46}{195} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{4}{3})& = & -5x+\frac{3}{7} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -5x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{-105x} +9 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{+105x} & = & \color{red}{-105x} +9 \color{blue}{+105x} \color{blue}{+56} \\\Leftrightarrow & 168x+105x& = & 9+56 \\\Leftrightarrow & \color{red}{273} x& = & 65 \\\Leftrightarrow & x = \frac{65}{273} & & \\\Leftrightarrow & x = \frac{5}{21} & & \\ & V = \left\{ \frac{5}{21} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{12})& = & -6x+\frac{3}{8} \\\Leftrightarrow & -35x-\frac{35}{12}& = & -6x+\frac{3}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-840}{ \color{blue}{24} }x- \frac{70}{ \color{blue}{24} })& = & (\frac{-144}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -840x \color{red}{-70} & = & \color{red}{-144x} +9 \\\Leftrightarrow & -840x \color{red}{-70} \color{blue}{+70} \color{blue}{+144x} & = & \color{red}{-144x} +9 \color{blue}{+144x} \color{blue}{+70} \\\Leftrightarrow & -840x+144x& = & 9+70 \\\Leftrightarrow & \color{red}{-696} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-696} & & \\\Leftrightarrow & x = \frac{-79}{696} & & \\ & V = \left\{ \frac{-79}{696} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{110}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-110} & = & \color{red}{-231x} +30 \\\Leftrightarrow & -660x \color{red}{-110} \color{blue}{+110} \color{blue}{+231x} & = & \color{red}{-231x} +30 \color{blue}{+231x} \color{blue}{+110} \\\Leftrightarrow & -660x+231x& = & 30+110 \\\Leftrightarrow & \color{red}{-429} x& = & 140 \\\Leftrightarrow & x = \frac{140}{-429} & & \\\Leftrightarrow & x = \frac{-140}{429} & & \\ & V = \left\{ \frac{-140}{429} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{6})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -15x+\frac{25}{6}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+25} & = & \color{red}{48x} +15 \\\Leftrightarrow & -90x \color{red}{+25} \color{blue}{-25} \color{blue}{-48x} & = & \color{red}{48x} +15 \color{blue}{-48x} \color{blue}{-25} \\\Leftrightarrow & -90x-48x& = & 15-25 \\\Leftrightarrow & \color{red}{-138} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-138} & & \\\Leftrightarrow & x = \frac{5}{69} & & \\ & V = \left\{ \frac{5}{69} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{+80} & = & \color{red}{210x} +9 \\\Leftrightarrow & -480x \color{red}{+80} \color{blue}{-80} \color{blue}{-210x} & = & \color{red}{210x} +9 \color{blue}{-210x} \color{blue}{-80} \\\Leftrightarrow & -480x-210x& = & 9-80 \\\Leftrightarrow & \color{red}{-690} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-690} & & \\\Leftrightarrow & x = \frac{71}{690} & & \\ & V = \left\{ \frac{71}{690} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{3})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{8}{3}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{+8} & = & \color{red}{21x} +8 \\\Leftrightarrow & -18x \color{red}{+8} \color{blue}{-8} \color{blue}{-21x} & = & \color{red}{21x} +8 \color{blue}{-21x} \color{blue}{-8} \\\Leftrightarrow & -18x-21x& = & 8-8 \\\Leftrightarrow & \color{red}{-39} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-39} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{15}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-45} & = & \color{red}{105x} +28 \\\Leftrightarrow & 252x \color{red}{-45} \color{blue}{+45} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{+45} \\\Leftrightarrow & 252x-105x& = & 28+45 \\\Leftrightarrow & \color{red}{147} x& = & 73 \\\Leftrightarrow & x = \frac{73}{147} & & \\ & V = \left\{ \frac{73}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{10})& = & -5x+\frac{3}{2} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+9} & = & \color{red}{-50x} +15 \\\Leftrightarrow & -120x \color{red}{+9} \color{blue}{-9} \color{blue}{+50x} & = & \color{red}{-50x} +15 \color{blue}{+50x} \color{blue}{-9} \\\Leftrightarrow & -120x+50x& = & 15-9 \\\Leftrightarrow & \color{red}{-70} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-70} & & \\\Leftrightarrow & x = \frac{-3}{35} & & \\ & V = \left\{ \frac{-3}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{3})& = & -3x+\frac{2}{11} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+88} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -264x \color{red}{+88} \color{blue}{-88} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-88} \\\Leftrightarrow & -264x+99x& = & 6-88 \\\Leftrightarrow & \color{red}{-165} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-165} & & \\\Leftrightarrow & x = \frac{82}{165} & & \\ & V = \left\{ \frac{82}{165} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{20}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-20} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 84x \color{red}{-20} \color{blue}{+20} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+20} \\\Leftrightarrow & 84x+35x& = & 6+20 \\\Leftrightarrow & \color{red}{119} x& = & 26 \\\Leftrightarrow & x = \frac{26}{119} & & \\ & V = \left\{ \frac{26}{119} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{5})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+132} & = & \color{red}{275x} +30 \\\Leftrightarrow & 990x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +30 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & 990x-275x& = & 30-132 \\\Leftrightarrow & \color{red}{715} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{715} & & \\ & V = \left\{ \frac{-102}{715} \right\} & \\\end{align}\)
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