Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 6x-\frac{4}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{-4} & = & \color{red}{25x} +4 \\\Leftrightarrow & 30x \color{red}{-4} \color{blue}{+4} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+4} \\\Leftrightarrow & 30x-25x& = & 4+4 \\\Leftrightarrow & \color{red}{5} x& = & 8 \\\Leftrightarrow & x = \frac{8}{5} & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & 8x+\frac{5}{7} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 8x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{105}{ \color{blue}{77} })& = & (\frac{616}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-105} & = & \color{red}{616x} +55 \\\Leftrightarrow & 1155x \color{red}{-105} \color{blue}{+105} \color{blue}{-616x} & = & \color{red}{616x} +55 \color{blue}{-616x} \color{blue}{+105} \\\Leftrightarrow & 1155x-616x& = & 55+105 \\\Leftrightarrow & \color{red}{539} x& = & 160 \\\Leftrightarrow & x = \frac{160}{539} & & \\ & V = \left\{ \frac{160}{539} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{25}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+25} & = & \color{red}{49x} +3 \\\Leftrightarrow & -70x \color{red}{+25} \color{blue}{-25} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-25} \\\Leftrightarrow & -70x-49x& = & 3-25 \\\Leftrightarrow & \color{red}{-119} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-119} & & \\\Leftrightarrow & x = \frac{22}{119} & & \\ & V = \left\{ \frac{22}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{3}{2})& = & 7x+\frac{5}{4} \\\Leftrightarrow & -20x+\frac{15}{2}& = & 7x+\frac{5}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-80}{ \color{blue}{4} }x+ \frac{30}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{5}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -80x \color{red}{+30} & = & \color{red}{28x} +5 \\\Leftrightarrow & -80x \color{red}{+30} \color{blue}{-30} \color{blue}{-28x} & = & \color{red}{28x} +5 \color{blue}{-28x} \color{blue}{-30} \\\Leftrightarrow & -80x-28x& = & 5-30 \\\Leftrightarrow & \color{red}{-108} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-108} & & \\\Leftrightarrow & x = \frac{25}{108} & & \\ & V = \left\{ \frac{25}{108} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{2})& = & -8x+\frac{7}{11} \\\Leftrightarrow & -21x-\frac{21}{2}& = & -8x+\frac{7}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{14}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-231} & = & \color{red}{-176x} +14 \\\Leftrightarrow & -462x \color{red}{-231} \color{blue}{+231} \color{blue}{+176x} & = & \color{red}{-176x} +14 \color{blue}{+176x} \color{blue}{+231} \\\Leftrightarrow & -462x+176x& = & 14+231 \\\Leftrightarrow & \color{red}{-286} x& = & 245 \\\Leftrightarrow & x = \frac{245}{-286} & & \\\Leftrightarrow & x = \frac{-245}{286} & & \\ & V = \left\{ \frac{-245}{286} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{8})& = & 9x+\frac{4}{5} \\\Leftrightarrow & -35x+\frac{21}{8}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{360x} +32 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-360x} & = & \color{red}{360x} +32 \color{blue}{-360x} \color{blue}{-105} \\\Leftrightarrow & -1400x-360x& = & 32-105 \\\Leftrightarrow & \color{red}{-1760} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-1760} & & \\\Leftrightarrow & x = \frac{73}{1760} & & \\ & V = \left\{ \frac{73}{1760} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{-231x} +49 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{+231x} & = & \color{red}{-231x} +49 \color{blue}{+231x} \color{blue}{-66} \\\Leftrightarrow & 616x+231x& = & 49-66 \\\Leftrightarrow & \color{red}{847} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{847} & & \\ & V = \left\{ \frac{-17}{847} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{-63} & = & \color{red}{120x} +28 \\\Leftrightarrow & 504x \color{red}{-63} \color{blue}{+63} \color{blue}{-120x} & = & \color{red}{120x} +28 \color{blue}{-120x} \color{blue}{+63} \\\Leftrightarrow & 504x-120x& = & 28+63 \\\Leftrightarrow & \color{red}{384} x& = & 91 \\\Leftrightarrow & x = \frac{91}{384} & & \\ & V = \left\{ \frac{91}{384} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{9})& = & -9x+\frac{7}{2} \\\Leftrightarrow & 20x-\frac{20}{9}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{63}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-40} & = & \color{red}{-162x} +63 \\\Leftrightarrow & 360x \color{red}{-40} \color{blue}{+40} \color{blue}{+162x} & = & \color{red}{-162x} +63 \color{blue}{+162x} \color{blue}{+40} \\\Leftrightarrow & 360x+162x& = & 63+40 \\\Leftrightarrow & \color{red}{522} x& = & 103 \\\Leftrightarrow & x = \frac{103}{522} & & \\ & V = \left\{ \frac{103}{522} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{4})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{+45} & = & \color{red}{-84x} +8 \\\Leftrightarrow & -120x \color{red}{+45} \color{blue}{-45} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{-45} \\\Leftrightarrow & -120x+84x& = & 8-45 \\\Leftrightarrow & \color{red}{-36} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-36} & & \\\Leftrightarrow & x = \frac{37}{36} & & \\ & V = \left\{ \frac{37}{36} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{-441x} +27 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{+441x} & = & \color{red}{-441x} +27 \color{blue}{+441x} \color{blue}{-56} \\\Leftrightarrow & -1008x+441x& = & 27-56 \\\Leftrightarrow & \color{red}{-567} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-567} & & \\\Leftrightarrow & x = \frac{29}{567} & & \\ & V = \left\{ \frac{29}{567} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{5})& = & -5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{18}{5}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-720}{ \color{blue}{60} }x- \frac{216}{ \color{blue}{60} })& = & (\frac{-300}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -720x \color{red}{-216} & = & \color{red}{-300x} +25 \\\Leftrightarrow & -720x \color{red}{-216} \color{blue}{+216} \color{blue}{+300x} & = & \color{red}{-300x} +25 \color{blue}{+300x} \color{blue}{+216} \\\Leftrightarrow & -720x+300x& = & 25+216 \\\Leftrightarrow & \color{red}{-420} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-420} & & \\\Leftrightarrow & x = \frac{-241}{420} & & \\ & V = \left\{ \frac{-241}{420} \right\} & \\\end{align}\)
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