Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{24}{11}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-72} & = & \color{red}{165x} +22 \\\Leftrightarrow & -396x \color{red}{-72} \color{blue}{+72} \color{blue}{-165x} & = & \color{red}{165x} +22 \color{blue}{-165x} \color{blue}{+72} \\\Leftrightarrow & -396x-165x& = & 22+72 \\\Leftrightarrow & \color{red}{-561} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-561} & & \\\Leftrightarrow & x = \frac{-94}{561} & & \\ & V = \left\{ \frac{-94}{561} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{11})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 16x+\frac{20}{11}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{1056}{ \color{blue}{66} }x+ \frac{120}{ \color{blue}{66} })& = & (\frac{-330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 1056x \color{red}{+120} & = & \color{red}{-330x} +55 \\\Leftrightarrow & 1056x \color{red}{+120} \color{blue}{-120} \color{blue}{+330x} & = & \color{red}{-330x} +55 \color{blue}{+330x} \color{blue}{-120} \\\Leftrightarrow & 1056x+330x& = & 55-120 \\\Leftrightarrow & \color{red}{1386} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{1386} & & \\ & V = \left\{ \frac{-65}{1386} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{49x} +6 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & -70x-49x& = & 6+10 \\\Leftrightarrow & \color{red}{-119} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-119} & & \\\Leftrightarrow & x = \frac{-16}{119} & & \\ & V = \left\{ \frac{-16}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & 4x+\frac{9}{5} \\\Leftrightarrow & 21x+\frac{28}{3}& = & 4x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+140} & = & \color{red}{60x} +27 \\\Leftrightarrow & 315x \color{red}{+140} \color{blue}{-140} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{-140} \\\Leftrightarrow & 315x-60x& = & 27-140 \\\Leftrightarrow & \color{red}{255} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{255} & & \\ & V = \left\{ \frac{-113}{255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{3}{7})& = & 3x+\frac{5}{3} \\\Leftrightarrow & 10x-\frac{6}{7}& = & 3x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-18} & = & \color{red}{63x} +35 \\\Leftrightarrow & 210x \color{red}{-18} \color{blue}{+18} \color{blue}{-63x} & = & \color{red}{63x} +35 \color{blue}{-63x} \color{blue}{+18} \\\Leftrightarrow & 210x-63x& = & 35+18 \\\Leftrightarrow & \color{red}{147} x& = & 53 \\\Leftrightarrow & x = \frac{53}{147} & & \\ & V = \left\{ \frac{53}{147} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{4}{5})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{360}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 360x \color{red}{+72} & = & \color{red}{150x} +25 \\\Leftrightarrow & 360x \color{red}{+72} \color{blue}{-72} \color{blue}{-150x} & = & \color{red}{150x} +25 \color{blue}{-150x} \color{blue}{-72} \\\Leftrightarrow & 360x-150x& = & 25-72 \\\Leftrightarrow & \color{red}{210} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{210} & & \\ & V = \left\{ \frac{-47}{210} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{3})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 28x+\frac{14}{3}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{+70} & = & \color{red}{-135x} +24 \\\Leftrightarrow & 420x \color{red}{+70} \color{blue}{-70} \color{blue}{+135x} & = & \color{red}{-135x} +24 \color{blue}{+135x} \color{blue}{-70} \\\Leftrightarrow & 420x+135x& = & 24-70 \\\Leftrightarrow & \color{red}{555} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{555} & & \\ & V = \left\{ \frac{-46}{555} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & -2x+\frac{8}{11} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -2x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+154} & = & \color{red}{-66x} +24 \\\Leftrightarrow & 1155x \color{red}{+154} \color{blue}{-154} \color{blue}{+66x} & = & \color{red}{-66x} +24 \color{blue}{+66x} \color{blue}{-154} \\\Leftrightarrow & 1155x+66x& = & 24-154 \\\Leftrightarrow & \color{red}{1221} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{1221} & & \\ & V = \left\{ \frac{-130}{1221} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 18x+\frac{12}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+84} & = & \color{red}{385x} +88 \\\Leftrightarrow & 1386x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & 1386x-385x& = & 88-84 \\\Leftrightarrow & \color{red}{1001} x& = & 4 \\\Leftrightarrow & x = \frac{4}{1001} & & \\ & V = \left\{ \frac{4}{1001} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{539x} +42 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & 770x-539x& = & 42+110 \\\Leftrightarrow & \color{red}{231} x& = & 152 \\\Leftrightarrow & x = \frac{152}{231} & & \\ & V = \left\{ \frac{152}{231} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{9}{8} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{9}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-432}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{81}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -432x \color{red}{+64} & = & \color{red}{504x} +81 \\\Leftrightarrow & -432x \color{red}{+64} \color{blue}{-64} \color{blue}{-504x} & = & \color{red}{504x} +81 \color{blue}{-504x} \color{blue}{-64} \\\Leftrightarrow & -432x-504x& = & 81-64 \\\Leftrightarrow & \color{red}{-936} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-936} & & \\\Leftrightarrow & x = \frac{-17}{936} & & \\ & V = \left\{ \frac{-17}{936} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -9x-\frac{15}{4}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{-45} & = & \color{red}{-60x} +16 \\\Leftrightarrow & -108x \color{red}{-45} \color{blue}{+45} \color{blue}{+60x} & = & \color{red}{-60x} +16 \color{blue}{+60x} \color{blue}{+45} \\\Leftrightarrow & -108x+60x& = & 16+45 \\\Leftrightarrow & \color{red}{-48} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-48} & & \\\Leftrightarrow & x = \frac{-61}{48} & & \\ & V = \left\{ \frac{-61}{48} \right\} & \\\end{align}\)
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