Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

  1. \(7(-x+\frac{4}{7})=3x+\frac{9}{4}\)
  2. \(5(5x+\frac{2}{5})=7x+\frac{3}{16}\)
  3. \(-2(-4x+\frac{2}{3})=x+\frac{9}{11}\)
  4. \((-x-\frac{3}{5})=5x+\frac{9}{11}\)
  5. \(-2(2x+\frac{4}{5})=9x+\frac{8}{13}\)
  6. \(-6(-3x+\frac{3}{8})=-7x+\frac{9}{13}\)
  7. \(-5(2x-\frac{2}{9})=-9x+\frac{2}{9}\)
  8. \(2(-4x+\frac{5}{16})=7x+\frac{9}{11}\)
  9. \(-2(-5x+\frac{4}{9})=7x+\frac{3}{16}\)
  10. \(5(-2x+\frac{2}{13})=7x+\frac{9}{8}\)
  11. \(6(5x+\frac{2}{5})=29x+\frac{2}{7}\)
  12. \(4(4x+\frac{5}{11})=3x+\frac{6}{13}\)

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-x+\frac{4}{7})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -7x+4& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(-7x+4)& = & (3x+\frac{9}{4}). \color{blue}{4} \\\Leftrightarrow & -28x \color{red}{+16} & = & \color{red}{12x} +9 \\\Leftrightarrow & -28x \color{red}{+16} \color{blue}{-16} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{-16} \\\Leftrightarrow & -28x-12x& = & 9-16 \\\Leftrightarrow & \color{red}{-40} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-40} & & \\\Leftrightarrow & x = \frac{7}{40} & & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{5})& = & 7x+\frac{3}{16} \\\Leftrightarrow & 25x+2& = & 7x+\frac{3}{16} \\ & & & \text{kgv van noemers 1 en 16 is 16} \\\Leftrightarrow & \color{blue}{16} .(25x+2)& = & (7x+\frac{3}{16}). \color{blue}{16} \\\Leftrightarrow & 400x \color{red}{+32} & = & \color{red}{112x} +3 \\\Leftrightarrow & 400x \color{red}{+32} \color{blue}{-32} \color{blue}{-112x} & = & \color{red}{112x} +3 \color{blue}{-112x} \color{blue}{-32} \\\Leftrightarrow & 400x-112x& = & 3-32 \\\Leftrightarrow & \color{red}{288} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{288} & & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{3})& = & x+\frac{9}{11} \\\Leftrightarrow & 8x-\frac{4}{3}& = & x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(8x-\frac{4}{3})& = & (x+\frac{9}{11}). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-44} & = & \color{red}{33x} +27 \\\Leftrightarrow & 264x \color{red}{-44} \color{blue}{+44} \color{blue}{-33x} & = & \color{red}{33x} +27 \color{blue}{-33x} \color{blue}{+44} \\\Leftrightarrow & 264x-33x& = & 27+44 \\\Leftrightarrow & \color{red}{231} x& = & 71 \\\Leftrightarrow & x = \frac{71}{231} & & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{} (-x-\frac{3}{5})& = & 5x+\frac{9}{11} \\\Leftrightarrow & -x-\frac{3}{5}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(-x-\frac{3}{5})& = & (5x+\frac{9}{11}). \color{blue}{55} \\\Leftrightarrow & -55x \color{red}{-33} & = & \color{red}{275x} +45 \\\Leftrightarrow & -55x \color{red}{-33} \color{blue}{+33} \color{blue}{-275x} & = & \color{red}{275x} +45 \color{blue}{-275x} \color{blue}{+33} \\\Leftrightarrow & -55x-275x& = & 45+33 \\\Leftrightarrow & \color{red}{-330} x& = & 78 \\\Leftrightarrow & x = \frac{78}{-330} & & \\\Leftrightarrow & x = \frac{-13}{55} & & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{5})& = & 9x+\frac{8}{13} \\\Leftrightarrow & -4x-\frac{8}{5}& = & 9x+\frac{8}{13} \\ & & & \text{kgv van noemers 5 en 13 is 65} \\\Leftrightarrow & \color{blue}{65} .(-4x-\frac{8}{5})& = & (9x+\frac{8}{13}). \color{blue}{65} \\\Leftrightarrow & -260x \color{red}{-104} & = & \color{red}{585x} +40 \\\Leftrightarrow & -260x \color{red}{-104} \color{blue}{+104} \color{blue}{-585x} & = & \color{red}{585x} +40 \color{blue}{-585x} \color{blue}{+104} \\\Leftrightarrow & -260x-585x& = & 40+104 \\\Leftrightarrow & \color{red}{-845} x& = & 144 \\\Leftrightarrow & x = \frac{144}{-845} & & \\\Leftrightarrow & x = \frac{-144}{845} & & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{3}{8})& = & -7x+\frac{9}{13} \\\Leftrightarrow & 18x-\frac{9}{4}& = & -7x+\frac{9}{13} \\ & & & \text{kgv van noemers 4 en 13 is 52} \\\Leftrightarrow & \color{blue}{52} .(18x-\frac{9}{4})& = & (-7x+\frac{9}{13}). \color{blue}{52} \\\Leftrightarrow & 936x \color{red}{-117} & = & \color{red}{-364x} +36 \\\Leftrightarrow & 936x \color{red}{-117} \color{blue}{+117} \color{blue}{+364x} & = & \color{red}{-364x} +36 \color{blue}{+364x} \color{blue}{+117} \\\Leftrightarrow & 936x+364x& = & 36+117 \\\Leftrightarrow & \color{red}{1300} x& = & 153 \\\Leftrightarrow & x = \frac{153}{1300} & & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{9})& = & -9x+\frac{2}{9} \\\Leftrightarrow & -10x+\frac{10}{9}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(-10x+\frac{10}{9})& = & (-9x+\frac{2}{9}). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+10} & = & \color{red}{-81x} +2 \\\Leftrightarrow & -90x \color{red}{+10} \color{blue}{-10} \color{blue}{+81x} & = & \color{red}{-81x} +2 \color{blue}{+81x} \color{blue}{-10} \\\Leftrightarrow & -90x+81x& = & 2-10 \\\Leftrightarrow & \color{red}{-9} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-9} & & \\\Leftrightarrow & x = \frac{8}{9} & & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{16})& = & 7x+\frac{9}{11} \\\Leftrightarrow & -8x+\frac{5}{8}& = & 7x+\frac{9}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(-8x+\frac{5}{8})& = & (7x+\frac{9}{11}). \color{blue}{88} \\\Leftrightarrow & -704x \color{red}{+55} & = & \color{red}{616x} +72 \\\Leftrightarrow & -704x \color{red}{+55} \color{blue}{-55} \color{blue}{-616x} & = & \color{red}{616x} +72 \color{blue}{-616x} \color{blue}{-55} \\\Leftrightarrow & -704x-616x& = & 72-55 \\\Leftrightarrow & \color{red}{-1320} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-1320} & & \\\Leftrightarrow & x = \frac{-17}{1320} & & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{9})& = & 7x+\frac{3}{16} \\\Leftrightarrow & 10x-\frac{8}{9}& = & 7x+\frac{3}{16} \\ & & & \text{kgv van noemers 9 en 16 is 144} \\\Leftrightarrow & \color{blue}{144} .(10x-\frac{8}{9})& = & (7x+\frac{3}{16}). \color{blue}{144} \\\Leftrightarrow & 1440x \color{red}{-128} & = & \color{red}{1008x} +27 \\\Leftrightarrow & 1440x \color{red}{-128} \color{blue}{+128} \color{blue}{-1008x} & = & \color{red}{1008x} +27 \color{blue}{-1008x} \color{blue}{+128} \\\Leftrightarrow & 1440x-1008x& = & 27+128 \\\Leftrightarrow & \color{red}{432} x& = & 155 \\\Leftrightarrow & x = \frac{155}{432} & & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{2}{13})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -10x+\frac{10}{13}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 13 en 8 is 104} \\\Leftrightarrow & \color{blue}{104} .(-10x+\frac{10}{13})& = & (7x+\frac{9}{8}). \color{blue}{104} \\\Leftrightarrow & -1040x \color{red}{+80} & = & \color{red}{728x} +117 \\\Leftrightarrow & -1040x \color{red}{+80} \color{blue}{-80} \color{blue}{-728x} & = & \color{red}{728x} +117 \color{blue}{-728x} \color{blue}{-80} \\\Leftrightarrow & -1040x-728x& = & 117-80 \\\Leftrightarrow & \color{red}{-1768} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-1768} & & \\\Leftrightarrow & x = \frac{-37}{1768} & & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{2}{5})& = & 29x+\frac{2}{7} \\\Leftrightarrow & 30x+\frac{12}{5}& = & 29x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(30x+\frac{12}{5})& = & (29x+\frac{2}{7}). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{+84} & = & \color{red}{1015x} +10 \\\Leftrightarrow & 1050x \color{red}{+84} \color{blue}{-84} \color{blue}{-1015x} & = & \color{red}{1015x} +10 \color{blue}{-1015x} \color{blue}{-84} \\\Leftrightarrow & 1050x-1015x& = & 10-84 \\\Leftrightarrow & \color{red}{35} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{35} & & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{11})& = & 3x+\frac{6}{13} \\\Leftrightarrow & 16x+\frac{20}{11}& = & 3x+\frac{6}{13} \\ & & & \text{kgv van noemers 11 en 13 is 143} \\\Leftrightarrow & \color{blue}{143} .(16x+\frac{20}{11})& = & (3x+\frac{6}{13}). \color{blue}{143} \\\Leftrightarrow & 2288x \color{red}{+260} & = & \color{red}{429x} +66 \\\Leftrightarrow & 2288x \color{red}{+260} \color{blue}{-260} \color{blue}{-429x} & = & \color{red}{429x} +66 \color{blue}{-429x} \color{blue}{-260} \\\Leftrightarrow & 2288x-429x& = & 66-260 \\\Leftrightarrow & \color{red}{1859} x& = & -194 \\\Leftrightarrow & x = \frac{-194}{1859} & & \\\end{align}\)
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 06:41:41