Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{4}{11})& = & 5x+\frac{4}{11} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{55x} +4 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-55x} & = & \color{red}{55x} +4 \color{blue}{-55x} \color{blue}{-24} \\\Leftrightarrow & -132x-55x& = & 4-24 \\\Leftrightarrow & \color{red}{-187} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-187} & & \\\Leftrightarrow & x = \frac{20}{187} & & \\ & V = \left\{ \frac{20}{187} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 16x-\frac{16}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{-48} & = & \color{red}{147x} +14 \\\Leftrightarrow & 336x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & 336x-147x& = & 14+48 \\\Leftrightarrow & \color{red}{189} x& = & 62 \\\Leftrightarrow & x = \frac{62}{189} & & \\ & V = \left\{ \frac{62}{189} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-240}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -240x \color{red}{-36} & = & \color{red}{105x} +25 \\\Leftrightarrow & -240x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -240x-105x& = & 25+36 \\\Leftrightarrow & \color{red}{-345} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-345} & & \\\Leftrightarrow & x = \frac{-61}{345} & & \\ & V = \left\{ \frac{-61}{345} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{5})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -21x+\frac{14}{5}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{42}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+42} & = & \color{red}{-120x} +20 \\\Leftrightarrow & -315x \color{red}{+42} \color{blue}{-42} \color{blue}{+120x} & = & \color{red}{-120x} +20 \color{blue}{+120x} \color{blue}{-42} \\\Leftrightarrow & -315x+120x& = & 20-42 \\\Leftrightarrow & \color{red}{-195} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-195} & & \\\Leftrightarrow & x = \frac{22}{195} & & \\ & V = \left\{ \frac{22}{195} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-98x} +63 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{+60} \\\Leftrightarrow & 420x+98x& = & 63+60 \\\Leftrightarrow & \color{red}{518} x& = & 123 \\\Leftrightarrow & x = \frac{123}{518} & & \\ & V = \left\{ \frac{123}{518} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{4}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -30x-\frac{24}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1890}{ \color{blue}{63} }x- \frac{216}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1890x \color{red}{-216} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -1890x \color{red}{-216} \color{blue}{+216} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{+216} \\\Leftrightarrow & -1890x+441x& = & 28+216 \\\Leftrightarrow & \color{red}{-1449} x& = & 244 \\\Leftrightarrow & x = \frac{244}{-1449} & & \\\Leftrightarrow & x = \frac{-244}{1449} & & \\ & V = \left\{ \frac{-244}{1449} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 20x+\frac{16}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{48}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+48} & = & \color{red}{45x} +20 \\\Leftrightarrow & 300x \color{red}{+48} \color{blue}{-48} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{-48} \\\Leftrightarrow & 300x-45x& = & 20-48 \\\Leftrightarrow & \color{red}{255} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{255} & & \\ & V = \left\{ \frac{-28}{255} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{10})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x+\frac{9}{10}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-120}{ \color{blue}{20} }x+ \frac{18}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -120x \color{red}{+18} & = & \color{red}{140x} +45 \\\Leftrightarrow & -120x \color{red}{+18} \color{blue}{-18} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{-18} \\\Leftrightarrow & -120x-140x& = & 45-18 \\\Leftrightarrow & \color{red}{-260} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-260} & & \\\Leftrightarrow & x = \frac{-27}{260} & & \\ & V = \left\{ \frac{-27}{260} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & -4x+\frac{7}{9} \\\Leftrightarrow & -15x+\frac{10}{7}& = & -4x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+90} & = & \color{red}{-252x} +49 \\\Leftrightarrow & -945x \color{red}{+90} \color{blue}{-90} \color{blue}{+252x} & = & \color{red}{-252x} +49 \color{blue}{+252x} \color{blue}{-90} \\\Leftrightarrow & -945x+252x& = & 49-90 \\\Leftrightarrow & \color{red}{-693} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-693} & & \\\Leftrightarrow & x = \frac{41}{693} & & \\ & V = \left\{ \frac{41}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{6})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 28x-\frac{35}{6}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{-35} & = & \color{red}{54x} +8 \\\Leftrightarrow & 168x \color{red}{-35} \color{blue}{+35} \color{blue}{-54x} & = & \color{red}{54x} +8 \color{blue}{-54x} \color{blue}{+35} \\\Leftrightarrow & 168x-54x& = & 8+35 \\\Leftrightarrow & \color{red}{114} x& = & 43 \\\Leftrightarrow & x = \frac{43}{114} & & \\ & V = \left\{ \frac{43}{114} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{7})& = & -8x+\frac{10}{9} \\\Leftrightarrow & -21x+4& = & -8x+\frac{10}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{36}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+36} & = & \color{red}{-72x} +10 \\\Leftrightarrow & -189x \color{red}{+36} \color{blue}{-36} \color{blue}{+72x} & = & \color{red}{-72x} +10 \color{blue}{+72x} \color{blue}{-36} \\\Leftrightarrow & -189x+72x& = & 10-36 \\\Leftrightarrow & \color{red}{-117} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-117} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+88} & = & \color{red}{-495x} +90 \\\Leftrightarrow & -396x \color{red}{+88} \color{blue}{-88} \color{blue}{+495x} & = & \color{red}{-495x} +90 \color{blue}{+495x} \color{blue}{-88} \\\Leftrightarrow & -396x+495x& = & 90-88 \\\Leftrightarrow & \color{red}{99} x& = & 2 \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
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