Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{5}{7})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 24x-\frac{30}{7}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-330} & = & \color{red}{385x} +21 \\\Leftrightarrow & 1848x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +21 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1848x-385x& = & 21+330 \\\Leftrightarrow & \color{red}{1463} x& = & 351 \\\Leftrightarrow & x = \frac{351}{1463} & & \\ & V = \left\{ \frac{351}{1463} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{3}{5})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{+12} & = & \color{red}{15x} +6 \\\Leftrightarrow & 80x \color{red}{+12} \color{blue}{-12} \color{blue}{-15x} & = & \color{red}{15x} +6 \color{blue}{-15x} \color{blue}{-12} \\\Leftrightarrow & 80x-15x& = & 6-12 \\\Leftrightarrow & \color{red}{65} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{65} & & \\ & V = \left\{ \frac{-6}{65} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{10}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-30} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -660x \color{red}{-30} \color{blue}{+30} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+30} \\\Leftrightarrow & -660x+231x& = & 22+30 \\\Leftrightarrow & \color{red}{-429} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-429} & & \\\Leftrightarrow & x = \frac{-4}{33} & & \\ & V = \left\{ \frac{-4}{33} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{7})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{8}{7}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{84}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 84x \color{red}{+16} & = & \color{red}{70x} +63 \\\Leftrightarrow & 84x \color{red}{+16} \color{blue}{-16} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-16} \\\Leftrightarrow & 84x-70x& = & 63-16 \\\Leftrightarrow & \color{red}{14} x& = & 47 \\\Leftrightarrow & x = \frac{47}{14} & & \\ & V = \left\{ \frac{47}{14} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +56 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +56 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 56-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1001} & & \\\Leftrightarrow & x = \frac{10}{1001} & & \\ & V = \left\{ \frac{10}{1001} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -9x+\frac{8}{3} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-60}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -60x \color{red}{+12} & = & \color{red}{-135x} +40 \\\Leftrightarrow & -60x \color{red}{+12} \color{blue}{-12} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{-12} \\\Leftrightarrow & -60x+135x& = & 40-12 \\\Leftrightarrow & \color{red}{75} x& = & 28 \\\Leftrightarrow & x = \frac{28}{75} & & \\ & V = \left\{ \frac{28}{75} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+8} & = & \color{red}{-63x} +6 \\\Leftrightarrow & 90x \color{red}{+8} \color{blue}{-8} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{-8} \\\Leftrightarrow & 90x+63x& = & 6-8 \\\Leftrightarrow & \color{red}{153} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{153} & & \\ & V = \left\{ \frac{-2}{153} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{4})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -35x-\frac{21}{4}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{42}{ \color{blue}{8} })& = & (\frac{-24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-42} & = & \color{red}{-24x} +7 \\\Leftrightarrow & -280x \color{red}{-42} \color{blue}{+42} \color{blue}{+24x} & = & \color{red}{-24x} +7 \color{blue}{+24x} \color{blue}{+42} \\\Leftrightarrow & -280x+24x& = & 7+42 \\\Leftrightarrow & \color{red}{-256} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-256} & & \\\Leftrightarrow & x = \frac{-49}{256} & & \\ & V = \left\{ \frac{-49}{256} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{5}{2})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -14x+\frac{35}{2}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x+ \frac{105}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{+105} & = & \color{red}{18x} +8 \\\Leftrightarrow & -84x \color{red}{+105} \color{blue}{-105} \color{blue}{-18x} & = & \color{red}{18x} +8 \color{blue}{-18x} \color{blue}{-105} \\\Leftrightarrow & -84x-18x& = & 8-105 \\\Leftrightarrow & \color{red}{-102} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-102} & & \\\Leftrightarrow & x = \frac{97}{102} & & \\ & V = \left\{ \frac{97}{102} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{+132} & = & \color{red}{385x} +10 \\\Leftrightarrow & -330x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -330x-385x& = & 10-132 \\\Leftrightarrow & \color{red}{-715} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{-715} & & \\\Leftrightarrow & x = \frac{122}{715} & & \\ & V = \left\{ \frac{122}{715} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{2})& = & -5x+\frac{7}{9} \\\Leftrightarrow & -12x+\frac{15}{2}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x+ \frac{135}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{+135} & = & \color{red}{-90x} +14 \\\Leftrightarrow & -216x \color{red}{+135} \color{blue}{-135} \color{blue}{+90x} & = & \color{red}{-90x} +14 \color{blue}{+90x} \color{blue}{-135} \\\Leftrightarrow & -216x+90x& = & 14-135 \\\Leftrightarrow & \color{red}{-126} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{-126} & & \\\Leftrightarrow & x = \frac{121}{126} & & \\ & V = \left\{ \frac{121}{126} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{4})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{+45} & = & \color{red}{-84x} +32 \\\Leftrightarrow & -72x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +32 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & -72x+84x& = & 32-45 \\\Leftrightarrow & \color{red}{12} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{12} & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
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