Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{9}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+27} & = & \color{red}{75x} +40 \\\Leftrightarrow & -180x \color{red}{+27} \color{blue}{-27} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-27} \\\Leftrightarrow & -180x-75x& = & 40-27 \\\Leftrightarrow & \color{red}{-255} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-255} & & \\\Leftrightarrow & x = \frac{-13}{255} & & \\ & V = \left\{ \frac{-13}{255} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{24}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{-24} & = & \color{red}{49x} +8 \\\Leftrightarrow & -210x \color{red}{-24} \color{blue}{+24} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{+24} \\\Leftrightarrow & -210x-49x& = & 8+24 \\\Leftrightarrow & \color{red}{-259} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-259} & & \\\Leftrightarrow & x = \frac{-32}{259} & & \\ & V = \left\{ \frac{-32}{259} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{6})& = & 9x+\frac{8}{5} \\\Leftrightarrow & 20x-\frac{25}{6}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{600}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 600x \color{red}{-125} & = & \color{red}{270x} +48 \\\Leftrightarrow & 600x \color{red}{-125} \color{blue}{+125} \color{blue}{-270x} & = & \color{red}{270x} +48 \color{blue}{-270x} \color{blue}{+125} \\\Leftrightarrow & 600x-270x& = & 48+125 \\\Leftrightarrow & \color{red}{330} x& = & 173 \\\Leftrightarrow & x = \frac{173}{330} & & \\ & V = \left\{ \frac{173}{330} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{11})& = & 4x+\frac{5}{8} \\\Leftrightarrow & 25x+\frac{20}{11}& = & 4x+\frac{5}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2200}{ \color{blue}{88} }x+ \frac{160}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{55}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2200x \color{red}{+160} & = & \color{red}{352x} +55 \\\Leftrightarrow & 2200x \color{red}{+160} \color{blue}{-160} \color{blue}{-352x} & = & \color{red}{352x} +55 \color{blue}{-352x} \color{blue}{-160} \\\Leftrightarrow & 2200x-352x& = & 55-160 \\\Leftrightarrow & \color{red}{1848} x& = & -105 \\\Leftrightarrow & x = \frac{-105}{1848} & & \\\Leftrightarrow & x = \frac{-5}{88} & & \\ & V = \left\{ \frac{-5}{88} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & 8x+\frac{10}{7} \\\Leftrightarrow & -15x-\frac{6}{7}& = & 8x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-6} & = & \color{red}{56x} +10 \\\Leftrightarrow & -105x \color{red}{-6} \color{blue}{+6} \color{blue}{-56x} & = & \color{red}{56x} +10 \color{blue}{-56x} \color{blue}{+6} \\\Leftrightarrow & -105x-56x& = & 10+6 \\\Leftrightarrow & \color{red}{-161} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-161} & & \\\Leftrightarrow & x = \frac{-16}{161} & & \\ & V = \left\{ \frac{-16}{161} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & 60x+21x& = & 10-20 \\\Leftrightarrow & \color{red}{81} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{81} & & \\ & V = \left\{ \frac{-10}{81} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-10} & = & \color{red}{21x} +6 \\\Leftrightarrow & 70x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +6 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & 70x-21x& = & 6+10 \\\Leftrightarrow & \color{red}{49} x& = & 16 \\\Leftrightarrow & x = \frac{16}{49} & & \\ & V = \left\{ \frac{16}{49} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{4}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+28} & = & \color{red}{175x} +20 \\\Leftrightarrow & 210x \color{red}{+28} \color{blue}{-28} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-28} \\\Leftrightarrow & 210x-175x& = & 20-28 \\\Leftrightarrow & \color{red}{35} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{5}{7})& = & -5x+\frac{8}{7} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{+30} \\\Leftrightarrow & -84x+35x& = & 8+30 \\\Leftrightarrow & \color{red}{-49} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-49} & & \\\Leftrightarrow & x = \frac{-38}{49} & & \\ & V = \left\{ \frac{-38}{49} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 24x+\frac{30}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+330} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 1848x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & 1848x+385x& = & 14-330 \\\Leftrightarrow & \color{red}{2233} x& = & -316 \\\Leftrightarrow & x = \frac{-316}{2233} & & \\ & V = \left\{ \frac{-316}{2233} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{840}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 840x \color{red}{-300} & = & \color{red}{350x} +21 \\\Leftrightarrow & 840x \color{red}{-300} \color{blue}{+300} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{+300} \\\Leftrightarrow & 840x-350x& = & 21+300 \\\Leftrightarrow & \color{red}{490} x& = & 321 \\\Leftrightarrow & x = \frac{321}{490} & & \\ & V = \left\{ \frac{321}{490} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-126} & = & \color{red}{539x} +33 \\\Leftrightarrow & -2310x \color{red}{-126} \color{blue}{+126} \color{blue}{-539x} & = & \color{red}{539x} +33 \color{blue}{-539x} \color{blue}{+126} \\\Leftrightarrow & -2310x-539x& = & 33+126 \\\Leftrightarrow & \color{red}{-2849} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-2849} & & \\\Leftrightarrow & x = \frac{-159}{2849} & & \\ & V = \left\{ \frac{-159}{2849} \right\} & \\\end{align}\)
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