Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{7})& = & -4x+\frac{2}{5} \\\Leftrightarrow & -25x+\frac{20}{7}& = & -4x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+100} & = & \color{red}{-140x} +14 \\\Leftrightarrow & -875x \color{red}{+100} \color{blue}{-100} \color{blue}{+140x} & = & \color{red}{-140x} +14 \color{blue}{+140x} \color{blue}{-100} \\\Leftrightarrow & -875x+140x& = & 14-100 \\\Leftrightarrow & \color{red}{-735} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-735} & & \\\Leftrightarrow & x = \frac{86}{735} & & \\ & V = \left\{ \frac{86}{735} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 20x-\frac{20}{9}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{126x} +21 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{+40} \\\Leftrightarrow & 360x-126x& = & 21+40 \\\Leftrightarrow & \color{red}{234} x& = & 61 \\\Leftrightarrow & x = \frac{61}{234} & & \\ & V = \left\{ \frac{61}{234} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{4}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 15x-\frac{12}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{660}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 660x \color{red}{-48} & = & \color{red}{308x} +77 \\\Leftrightarrow & 660x \color{red}{-48} \color{blue}{+48} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{+48} \\\Leftrightarrow & 660x-308x& = & 77+48 \\\Leftrightarrow & \color{red}{352} x& = & 125 \\\Leftrightarrow & x = \frac{125}{352} & & \\ & V = \left\{ \frac{125}{352} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{7})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{15}{7}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-45} & = & \color{red}{-84x} +56 \\\Leftrightarrow & -315x \color{red}{-45} \color{blue}{+45} \color{blue}{+84x} & = & \color{red}{-84x} +56 \color{blue}{+84x} \color{blue}{+45} \\\Leftrightarrow & -315x+84x& = & 56+45 \\\Leftrightarrow & \color{red}{-231} x& = & 101 \\\Leftrightarrow & x = \frac{101}{-231} & & \\\Leftrightarrow & x = \frac{-101}{231} & & \\ & V = \left\{ \frac{-101}{231} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{4}{3}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{-105x} +30 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{+105x} & = & \color{red}{-105x} +30 \color{blue}{+105x} \color{blue}{+28} \\\Leftrightarrow & 126x+105x& = & 30+28 \\\Leftrightarrow & \color{red}{231} x& = & 58 \\\Leftrightarrow & x = \frac{58}{231} & & \\ & V = \left\{ \frac{58}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{2}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -28x+\frac{14}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{42}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+42} & = & \color{red}{-99x} +88 \\\Leftrightarrow & -924x \color{red}{+42} \color{blue}{-42} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{-42} \\\Leftrightarrow & -924x+99x& = & 88-42 \\\Leftrightarrow & \color{red}{-825} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-825} & & \\\Leftrightarrow & x = \frac{-46}{825} & & \\ & V = \left\{ \frac{-46}{825} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-216x} +16 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +16 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & -672x+216x& = & 16-63 \\\Leftrightarrow & \color{red}{-456} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-456} & & \\\Leftrightarrow & x = \frac{47}{456} & & \\ & V = \left\{ \frac{47}{456} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{2}{7})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 24x-\frac{12}{7}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 168x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 168x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{133} x& = & 18 \\\Leftrightarrow & x = \frac{18}{133} & & \\ & V = \left\{ \frac{18}{133} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{6})& = & 8x+\frac{5}{12} \\\Leftrightarrow & 15x+\frac{25}{6}& = & 8x+\frac{5}{12} \\ & & & \text{kgv van noemers 6 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{50}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+50} & = & \color{red}{96x} +5 \\\Leftrightarrow & 180x \color{red}{+50} \color{blue}{-50} \color{blue}{-96x} & = & \color{red}{96x} +5 \color{blue}{-96x} \color{blue}{-50} \\\Leftrightarrow & 180x-96x& = & 5-50 \\\Leftrightarrow & \color{red}{84} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{84} & & \\\Leftrightarrow & x = \frac{-15}{28} & & \\ & V = \left\{ \frac{-15}{28} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{9})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{4}{9}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-594}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -594x \color{red}{+44} & = & \color{red}{693x} +54 \\\Leftrightarrow & -594x \color{red}{+44} \color{blue}{-44} \color{blue}{-693x} & = & \color{red}{693x} +54 \color{blue}{-693x} \color{blue}{-44} \\\Leftrightarrow & -594x-693x& = & 54-44 \\\Leftrightarrow & \color{red}{-1287} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-1287} & & \\\Leftrightarrow & x = \frac{-10}{1287} & & \\ & V = \left\{ \frac{-10}{1287} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & 7x+\frac{7}{5} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{35x} +7 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +7 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & -80x-35x& = & 7+12 \\\Leftrightarrow & \color{red}{-115} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-115} & & \\\Leftrightarrow & x = \frac{-19}{115} & & \\ & V = \left\{ \frac{-19}{115} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{40}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 40x \color{red}{-4} & = & \color{red}{35x} +6 \\\Leftrightarrow & 40x \color{red}{-4} \color{blue}{+4} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+4} \\\Leftrightarrow & 40x-35x& = & 6+4 \\\Leftrightarrow & \color{red}{5} x& = & 10 \\\Leftrightarrow & x = \frac{10}{5} & & \\\Leftrightarrow & x = 2 & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
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