Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{6}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-6} & = & \color{red}{-35x} +10 \\\Leftrightarrow & -84x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & -84x+35x& = & 10+6 \\\Leftrightarrow & \color{red}{-49} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-49} & & \\\Leftrightarrow & x = \frac{-16}{49} & & \\ & V = \left\{ \frac{-16}{49} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{5})& = & -2x+\frac{7}{2} \\\Leftrightarrow & -28x+\frac{28}{5}& = & -2x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x+ \frac{56}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{+56} & = & \color{red}{-20x} +35 \\\Leftrightarrow & -280x \color{red}{+56} \color{blue}{-56} \color{blue}{+20x} & = & \color{red}{-20x} +35 \color{blue}{+20x} \color{blue}{-56} \\\Leftrightarrow & -280x+20x& = & 35-56 \\\Leftrightarrow & \color{red}{-260} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-260} & & \\\Leftrightarrow & x = \frac{21}{260} & & \\ & V = \left\{ \frac{21}{260} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 210x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & 210x+245x& = & 42+50 \\\Leftrightarrow & \color{red}{455} x& = & 92 \\\Leftrightarrow & x = \frac{92}{455} & & \\ & V = \left\{ \frac{92}{455} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -168x \color{red}{-21} & = & \color{red}{64x} +20 \\\Leftrightarrow & -168x \color{red}{-21} \color{blue}{+21} \color{blue}{-64x} & = & \color{red}{64x} +20 \color{blue}{-64x} \color{blue}{+21} \\\Leftrightarrow & -168x-64x& = & 20+21 \\\Leftrightarrow & \color{red}{-232} x& = & 41 \\\Leftrightarrow & x = \frac{41}{-232} & & \\\Leftrightarrow & x = \frac{-41}{232} & & \\ & V = \left\{ \frac{-41}{232} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -4x+\frac{7}{9} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+90} & = & \color{red}{-252x} +49 \\\Leftrightarrow & -945x \color{red}{+90} \color{blue}{-90} \color{blue}{+252x} & = & \color{red}{-252x} +49 \color{blue}{+252x} \color{blue}{-90} \\\Leftrightarrow & -945x+252x& = & 49-90 \\\Leftrightarrow & \color{red}{-693} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-693} & & \\\Leftrightarrow & x = \frac{41}{693} & & \\ & V = \left\{ \frac{41}{693} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -8x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -8x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -105x \color{red}{+10} & = & \color{red}{-56x} +8 \\\Leftrightarrow & -105x \color{red}{+10} \color{blue}{-10} \color{blue}{+56x} & = & \color{red}{-56x} +8 \color{blue}{+56x} \color{blue}{-10} \\\Leftrightarrow & -105x+56x& = & 8-10 \\\Leftrightarrow & \color{red}{-49} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-49} & & \\\Leftrightarrow & x = \frac{2}{49} & & \\ & V = \left\{ \frac{2}{49} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & 3x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{8}{9}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+16} & = & \color{red}{54x} +81 \\\Leftrightarrow & 180x \color{red}{+16} \color{blue}{-16} \color{blue}{-54x} & = & \color{red}{54x} +81 \color{blue}{-54x} \color{blue}{-16} \\\Leftrightarrow & 180x-54x& = & 81-16 \\\Leftrightarrow & \color{red}{126} x& = & 65 \\\Leftrightarrow & x = \frac{65}{126} & & \\ & V = \left\{ \frac{65}{126} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+20} & = & \color{red}{-15x} +8 \\\Leftrightarrow & -36x \color{red}{+20} \color{blue}{-20} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{-20} \\\Leftrightarrow & -36x+15x& = & 8-20 \\\Leftrightarrow & \color{red}{-21} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-21} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & -9x+\frac{10}{3} \\\Leftrightarrow & -8x+\frac{4}{5}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+12} & = & \color{red}{-135x} +50 \\\Leftrightarrow & -120x \color{red}{+12} \color{blue}{-12} \color{blue}{+135x} & = & \color{red}{-135x} +50 \color{blue}{+135x} \color{blue}{-12} \\\Leftrightarrow & -120x+135x& = & 50-12 \\\Leftrightarrow & \color{red}{15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{15} & & \\ & V = \left\{ \frac{38}{15} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{3})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 25x-\frac{10}{3}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{75}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 75x \color{red}{-10} & = & \color{red}{24x} +8 \\\Leftrightarrow & 75x \color{red}{-10} \color{blue}{+10} \color{blue}{-24x} & = & \color{red}{24x} +8 \color{blue}{-24x} \color{blue}{+10} \\\Leftrightarrow & 75x-24x& = & 8+10 \\\Leftrightarrow & \color{red}{51} x& = & 18 \\\Leftrightarrow & x = \frac{18}{51} & & \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{4})& = & -8x+\frac{4}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{-352x} +16 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{+352x} & = & \color{red}{-352x} +16 \color{blue}{+352x} \color{blue}{-165} \\\Leftrightarrow & -660x+352x& = & 16-165 \\\Leftrightarrow & \color{red}{-308} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{-308} & & \\\Leftrightarrow & x = \frac{149}{308} & & \\ & V = \left\{ \frac{149}{308} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{10})& = & 2x+\frac{5}{9} \\\Leftrightarrow & -28x+\frac{21}{10}& = & 2x+\frac{5}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-2520}{ \color{blue}{90} }x+ \frac{189}{ \color{blue}{90} })& = & (\frac{180}{ \color{blue}{90} }x+ \frac{50}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -2520x \color{red}{+189} & = & \color{red}{180x} +50 \\\Leftrightarrow & -2520x \color{red}{+189} \color{blue}{-189} \color{blue}{-180x} & = & \color{red}{180x} +50 \color{blue}{-180x} \color{blue}{-189} \\\Leftrightarrow & -2520x-180x& = & 50-189 \\\Leftrightarrow & \color{red}{-2700} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-2700} & & \\\Leftrightarrow & x = \frac{139}{2700} & & \\ & V = \left\{ \frac{139}{2700} \right\} & \\\end{align}\)
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