Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{11})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 30x-\frac{18}{11}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-126} & = & \color{red}{-539x} +22 \\\Leftrightarrow & 2310x \color{red}{-126} \color{blue}{+126} \color{blue}{+539x} & = & \color{red}{-539x} +22 \color{blue}{+539x} \color{blue}{+126} \\\Leftrightarrow & 2310x+539x& = & 22+126 \\\Leftrightarrow & \color{red}{2849} x& = & 148 \\\Leftrightarrow & x = \frac{148}{2849} & & \\\Leftrightarrow & x = \frac{4}{77} & & \\ & V = \left\{ \frac{4}{77} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 6x+\frac{4}{11} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 6x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{385}{ \color{blue}{99} })& = & (\frac{594}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-385} & = & \color{red}{594x} +36 \\\Leftrightarrow & -3465x \color{red}{-385} \color{blue}{+385} \color{blue}{-594x} & = & \color{red}{594x} +36 \color{blue}{-594x} \color{blue}{+385} \\\Leftrightarrow & -3465x-594x& = & 36+385 \\\Leftrightarrow & \color{red}{-4059} x& = & 421 \\\Leftrightarrow & x = \frac{421}{-4059} & & \\\Leftrightarrow & x = \frac{-421}{4059} & & \\ & V = \left\{ \frac{-421}{4059} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+2)& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x-14& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x- \frac{42}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{-42} & = & \color{red}{-9x} +10 \\\Leftrightarrow & -42x \color{red}{-42} \color{blue}{+42} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{+42} \\\Leftrightarrow & -42x+9x& = & 10+42 \\\Leftrightarrow & \color{red}{-33} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-33} & & \\\Leftrightarrow & x = \frac{-52}{33} & & \\ & V = \left\{ \frac{-52}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -5x+\frac{8}{9} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{-135} & = & \color{red}{-180x} +32 \\\Leftrightarrow & 216x \color{red}{-135} \color{blue}{+135} \color{blue}{+180x} & = & \color{red}{-180x} +32 \color{blue}{+180x} \color{blue}{+135} \\\Leftrightarrow & 216x+180x& = & 32+135 \\\Leftrightarrow & \color{red}{396} x& = & 167 \\\Leftrightarrow & x = \frac{167}{396} & & \\ & V = \left\{ \frac{167}{396} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & 5x+\frac{4}{11} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+110} & = & \color{red}{385x} +28 \\\Leftrightarrow & 462x \color{red}{+110} \color{blue}{-110} \color{blue}{-385x} & = & \color{red}{385x} +28 \color{blue}{-385x} \color{blue}{-110} \\\Leftrightarrow & 462x-385x& = & 28-110 \\\Leftrightarrow & \color{red}{77} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{77} & & \\ & V = \left\{ \frac{-82}{77} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{11})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 25x+\frac{10}{11}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1375}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1375x \color{red}{+50} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 1375x \color{red}{+50} \color{blue}{-50} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-50} \\\Leftrightarrow & 1375x+165x& = & 44-50 \\\Leftrightarrow & \color{red}{1540} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{1540} & & \\\Leftrightarrow & x = \frac{-3}{770} & & \\ & V = \left\{ \frac{-3}{770} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-63} & = & \color{red}{120x} +16 \\\Leftrightarrow & 672x \color{red}{-63} \color{blue}{+63} \color{blue}{-120x} & = & \color{red}{120x} +16 \color{blue}{-120x} \color{blue}{+63} \\\Leftrightarrow & 672x-120x& = & 16+63 \\\Leftrightarrow & \color{red}{552} x& = & 79 \\\Leftrightarrow & x = \frac{79}{552} & & \\ & V = \left\{ \frac{79}{552} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & 5x+\frac{2}{5} \\\Leftrightarrow & 12x-\frac{16}{7}& = & 5x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-80} & = & \color{red}{175x} +14 \\\Leftrightarrow & 420x \color{red}{-80} \color{blue}{+80} \color{blue}{-175x} & = & \color{red}{175x} +14 \color{blue}{-175x} \color{blue}{+80} \\\Leftrightarrow & 420x-175x& = & 14+80 \\\Leftrightarrow & \color{red}{245} x& = & 94 \\\Leftrightarrow & x = \frac{94}{245} & & \\ & V = \left\{ \frac{94}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+10} & = & \color{red}{35x} +10 \\\Leftrightarrow & 56x \color{red}{+10} \color{blue}{-10} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-10} \\\Leftrightarrow & 56x-35x& = & 10-10 \\\Leftrightarrow & \color{red}{21} x& = & 0 \\\Leftrightarrow & x = \frac{0}{21} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{16}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{120x} +16 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{-120x} & = & \color{red}{120x} +16 \color{blue}{-120x} \color{blue}{-63} \\\Leftrightarrow & 504x-120x& = & 16-63 \\\Leftrightarrow & \color{red}{384} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{384} & & \\ & V = \left\{ \frac{-47}{384} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{9})& = & -3x+\frac{3}{2} \\\Leftrightarrow & 4x-\frac{10}{9}& = & -3x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{72}{ \color{blue}{18} }x- \frac{20}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 72x \color{red}{-20} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 72x \color{red}{-20} \color{blue}{+20} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{+20} \\\Leftrightarrow & 72x+54x& = & 27+20 \\\Leftrightarrow & \color{red}{126} x& = & 47 \\\Leftrightarrow & x = \frac{47}{126} & & \\ & V = \left\{ \frac{47}{126} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{2}{7})& = & -4x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -4x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 189x \color{red}{+18} & = & \color{red}{-84x} +70 \\\Leftrightarrow & 189x \color{red}{+18} \color{blue}{-18} \color{blue}{+84x} & = & \color{red}{-84x} +70 \color{blue}{+84x} \color{blue}{-18} \\\Leftrightarrow & 189x+84x& = & 70-18 \\\Leftrightarrow & \color{red}{273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{273} & & \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
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