Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{7})& = & 8x+\frac{2}{7} \\\Leftrightarrow & -15x-\frac{25}{7}& = & 8x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x- \frac{25}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{-25} & = & \color{red}{56x} +2 \\\Leftrightarrow & -105x \color{red}{-25} \color{blue}{+25} \color{blue}{-56x} & = & \color{red}{56x} +2 \color{blue}{-56x} \color{blue}{+25} \\\Leftrightarrow & -105x-56x& = & 2+25 \\\Leftrightarrow & \color{red}{-161} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-161} & & \\\Leftrightarrow & x = \frac{-27}{161} & & \\ & V = \left\{ \frac{-27}{161} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{2}{7})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{+90} & = & \color{red}{441x} +49 \\\Leftrightarrow & 1260x \color{red}{+90} \color{blue}{-90} \color{blue}{-441x} & = & \color{red}{441x} +49 \color{blue}{-441x} \color{blue}{-90} \\\Leftrightarrow & 1260x-441x& = & 49-90 \\\Leftrightarrow & \color{red}{819} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{819} & & \\ & V = \left\{ \frac{-41}{819} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{9})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{28}{9}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{252}{ \color{blue}{9} }x+ \frac{28}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{81x} +30 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{-81x} & = & \color{red}{81x} +30 \color{blue}{-81x} \color{blue}{-28} \\\Leftrightarrow & 252x-81x& = & 30-28 \\\Leftrightarrow & \color{red}{171} x& = & 2 \\\Leftrightarrow & x = \frac{2}{171} & & \\ & V = \left\{ \frac{2}{171} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{2}{9})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{10}{9}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+10} & = & \color{red}{63x} +4 \\\Leftrightarrow & 90x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & 90x-63x& = & 4-10 \\\Leftrightarrow & \color{red}{27} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{27} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{10}{9} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-216} & = & \color{red}{-225x} +50 \\\Leftrightarrow & 540x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +50 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 540x+225x& = & 50+216 \\\Leftrightarrow & \color{red}{765} x& = & 266 \\\Leftrightarrow & x = \frac{266}{765} & & \\ & V = \left\{ \frac{266}{765} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{9})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1152}{ \color{blue}{72} }x+ \frac{160}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1152x \color{red}{+160} & = & \color{red}{504x} +63 \\\Leftrightarrow & -1152x \color{red}{+160} \color{blue}{-160} \color{blue}{-504x} & = & \color{red}{504x} +63 \color{blue}{-504x} \color{blue}{-160} \\\Leftrightarrow & -1152x-504x& = & 63-160 \\\Leftrightarrow & \color{red}{-1656} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-1656} & & \\\Leftrightarrow & x = \frac{97}{1656} & & \\ & V = \left\{ \frac{97}{1656} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{+18} & = & \color{red}{231x} +110 \\\Leftrightarrow & -198x \color{red}{+18} \color{blue}{-18} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-18} \\\Leftrightarrow & -198x-231x& = & 110-18 \\\Leftrightarrow & \color{red}{-429} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-429} & & \\\Leftrightarrow & x = \frac{-92}{429} & & \\ & V = \left\{ \frac{-92}{429} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x+\frac{24}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+24} & = & \color{red}{35x} +8 \\\Leftrightarrow & 84x \color{red}{+24} \color{blue}{-24} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{-24} \\\Leftrightarrow & 84x-35x& = & 8-24 \\\Leftrightarrow & \color{red}{49} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{49} & & \\ & V = \left\{ \frac{-16}{49} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{3}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{120}{ \color{blue}{6} }x- \frac{32}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 120x \color{red}{-32} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 120x \color{red}{-32} \color{blue}{+32} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{+32} \\\Leftrightarrow & 120x+42x& = & 27+32 \\\Leftrightarrow & \color{red}{162} x& = & 59 \\\Leftrightarrow & x = \frac{59}{162} & & \\ & V = \left\{ \frac{59}{162} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 4x+\frac{3}{2} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 4x+\frac{3}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{16}{ \color{blue}{4} }x+ \frac{6}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+15} & = & \color{red}{16x} +6 \\\Leftrightarrow & 60x \color{red}{+15} \color{blue}{-15} \color{blue}{-16x} & = & \color{red}{16x} +6 \color{blue}{-16x} \color{blue}{-15} \\\Leftrightarrow & 60x-16x& = & 6-15 \\\Leftrightarrow & \color{red}{44} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{44} & & \\ & V = \left\{ \frac{-9}{44} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & 7x+\frac{9}{2} \\\Leftrightarrow & 4x-\frac{10}{7}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{-20} & = & \color{red}{98x} +63 \\\Leftrightarrow & 56x \color{red}{-20} \color{blue}{+20} \color{blue}{-98x} & = & \color{red}{98x} +63 \color{blue}{-98x} \color{blue}{+20} \\\Leftrightarrow & 56x-98x& = & 63+20 \\\Leftrightarrow & \color{red}{-42} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-42} & & \\\Leftrightarrow & x = \frac{-83}{42} & & \\ & V = \left\{ \frac{-83}{42} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{1}{2})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 21x-\frac{7}{2}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{294}{ \color{blue}{14} }x- \frac{49}{ \color{blue}{14} })& = & (\frac{28}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 294x \color{red}{-49} & = & \color{red}{28x} +20 \\\Leftrightarrow & 294x \color{red}{-49} \color{blue}{+49} \color{blue}{-28x} & = & \color{red}{28x} +20 \color{blue}{-28x} \color{blue}{+49} \\\Leftrightarrow & 294x-28x& = & 20+49 \\\Leftrightarrow & \color{red}{266} x& = & 69 \\\Leftrightarrow & x = \frac{69}{266} & & \\ & V = \left\{ \frac{69}{266} \right\} & \\\end{align}\)
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