Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-132} & = & \color{red}{-385x} +10 \\\Leftrightarrow & -1320x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -1320x+385x& = & 10+132 \\\Leftrightarrow & \color{red}{-935} x& = & 142 \\\Leftrightarrow & x = \frac{142}{-935} & & \\\Leftrightarrow & x = \frac{-142}{935} & & \\ & V = \left\{ \frac{-142}{935} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{11})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{15}{11}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+45} & = & \color{red}{66x} +110 \\\Leftrightarrow & 825x \color{red}{+45} \color{blue}{-45} \color{blue}{-66x} & = & \color{red}{66x} +110 \color{blue}{-66x} \color{blue}{-45} \\\Leftrightarrow & 825x-66x& = & 110-45 \\\Leftrightarrow & \color{red}{759} x& = & 65 \\\Leftrightarrow & x = \frac{65}{759} & & \\ & V = \left\{ \frac{65}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 10x-\frac{20}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-60} & = & \color{red}{-147x} +70 \\\Leftrightarrow & 210x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & 210x+147x& = & 70+60 \\\Leftrightarrow & \color{red}{357} x& = & 130 \\\Leftrightarrow & x = \frac{130}{357} & & \\ & V = \left\{ \frac{130}{357} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -210x+147x& = & 56-30 \\\Leftrightarrow & \color{red}{-63} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-63} & & \\\Leftrightarrow & x = \frac{-26}{63} & & \\ & V = \left\{ \frac{-26}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{4}{7})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 10x+\frac{20}{7}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+60} & = & \color{red}{189x} +70 \\\Leftrightarrow & 210x \color{red}{+60} \color{blue}{-60} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{-60} \\\Leftrightarrow & 210x-189x& = & 70-60 \\\Leftrightarrow & \color{red}{21} x& = & 10 \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-30} & = & \color{red}{105x} +42 \\\Leftrightarrow & 350x \color{red}{-30} \color{blue}{+30} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+30} \\\Leftrightarrow & 350x-105x& = & 42+30 \\\Leftrightarrow & \color{red}{245} x& = & 72 \\\Leftrightarrow & x = \frac{72}{245} & & \\ & V = \left\{ \frac{72}{245} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{6}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{539x} +44 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+42} \\\Leftrightarrow & -462x-539x& = & 44+42 \\\Leftrightarrow & \color{red}{-1001} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-1001} & & \\\Leftrightarrow & x = \frac{-86}{1001} & & \\ & V = \left\{ \frac{-86}{1001} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x- \frac{350}{ \color{blue}{30} })& = & (\frac{240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{-350} & = & \color{red}{240x} +27 \\\Leftrightarrow & -630x \color{red}{-350} \color{blue}{+350} \color{blue}{-240x} & = & \color{red}{240x} +27 \color{blue}{-240x} \color{blue}{+350} \\\Leftrightarrow & -630x-240x& = & 27+350 \\\Leftrightarrow & \color{red}{-870} x& = & 377 \\\Leftrightarrow & x = \frac{377}{-870} & & \\\Leftrightarrow & x = \frac{-13}{30} & & \\ & V = \left\{ \frac{-13}{30} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+80} & = & \color{red}{315x} +56 \\\Leftrightarrow & -280x \color{red}{+80} \color{blue}{-80} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-80} \\\Leftrightarrow & -280x-315x& = & 56-80 \\\Leftrightarrow & \color{red}{-595} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{-595} & & \\\Leftrightarrow & x = \frac{24}{595} & & \\ & V = \left\{ \frac{24}{595} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & -9x+\frac{4}{5} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{24}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{-270x} +24 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{+270x} & = & \color{red}{-270x} +24 \color{blue}{+270x} \color{blue}{+175} \\\Leftrightarrow & 420x+270x& = & 24+175 \\\Leftrightarrow & \color{red}{690} x& = & 199 \\\Leftrightarrow & x = \frac{199}{690} & & \\ & V = \left\{ \frac{199}{690} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{2}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 24x+\frac{12}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+36} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 792x \color{red}{+36} \color{blue}{-36} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-36} \\\Leftrightarrow & 792x+165x& = & 22-36 \\\Leftrightarrow & \color{red}{957} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{957} & & \\ & V = \left\{ \frac{-14}{957} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+12} \\\Leftrightarrow & -150x+35x& = & 8+12 \\\Leftrightarrow & \color{red}{-115} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-115} & & \\\Leftrightarrow & x = \frac{-4}{23} & & \\ & V = \left\{ \frac{-4}{23} \right\} & \\\end{align}\)
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