Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{9}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+63} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -420x \color{red}{+63} \color{blue}{-63} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{-63} \\\Leftrightarrow & -420x+175x& = & 50-63 \\\Leftrightarrow & \color{red}{-245} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-245} & & \\\Leftrightarrow & x = \frac{13}{245} & & \\ & V = \left\{ \frac{13}{245} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{3}{2})& = & -6x+\frac{6}{7} \\\Leftrightarrow & 35x-\frac{21}{2}& = & -6x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{490}{ \color{blue}{14} }x- \frac{147}{ \color{blue}{14} })& = & (\frac{-84}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 490x \color{red}{-147} & = & \color{red}{-84x} +12 \\\Leftrightarrow & 490x \color{red}{-147} \color{blue}{+147} \color{blue}{+84x} & = & \color{red}{-84x} +12 \color{blue}{+84x} \color{blue}{+147} \\\Leftrightarrow & 490x+84x& = & 12+147 \\\Leftrightarrow & \color{red}{574} x& = & 159 \\\Leftrightarrow & x = \frac{159}{574} & & \\ & V = \left\{ \frac{159}{574} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{4}{9})& = & -5x+\frac{5}{12} \\\Leftrightarrow & 4x-\frac{8}{9}& = & -5x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{144}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 144x \color{red}{-32} & = & \color{red}{-180x} +15 \\\Leftrightarrow & 144x \color{red}{-32} \color{blue}{+32} \color{blue}{+180x} & = & \color{red}{-180x} +15 \color{blue}{+180x} \color{blue}{+32} \\\Leftrightarrow & 144x+180x& = & 15+32 \\\Leftrightarrow & \color{red}{324} x& = & 47 \\\Leftrightarrow & x = \frac{47}{324} & & \\ & V = \left\{ \frac{47}{324} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x+\frac{24}{11}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+24} & = & \color{red}{55x} +8 \\\Leftrightarrow & 132x \color{red}{+24} \color{blue}{-24} \color{blue}{-55x} & = & \color{red}{55x} +8 \color{blue}{-55x} \color{blue}{-24} \\\Leftrightarrow & 132x-55x& = & 8-24 \\\Leftrightarrow & \color{red}{77} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{77} & & \\ & V = \left\{ \frac{-16}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{7})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{63x} +14 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{-63x} & = & \color{red}{63x} +14 \color{blue}{-63x} \color{blue}{-30} \\\Leftrightarrow & 525x-63x& = & 14-30 \\\Leftrightarrow & \color{red}{462} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{462} & & \\\Leftrightarrow & x = \frac{-8}{231} & & \\ & V = \left\{ \frac{-8}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & -3x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{20}{3}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-96}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -96x \color{red}{-80} & = & \color{red}{-36x} +27 \\\Leftrightarrow & -96x \color{red}{-80} \color{blue}{+80} \color{blue}{+36x} & = & \color{red}{-36x} +27 \color{blue}{+36x} \color{blue}{+80} \\\Leftrightarrow & -96x+36x& = & 27+80 \\\Leftrightarrow & \color{red}{-60} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-60} & & \\\Leftrightarrow & x = \frac{-107}{60} & & \\ & V = \left\{ \frac{-107}{60} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+264} & = & \color{red}{-275x} +20 \\\Leftrightarrow & 990x \color{red}{+264} \color{blue}{-264} \color{blue}{+275x} & = & \color{red}{-275x} +20 \color{blue}{+275x} \color{blue}{-264} \\\Leftrightarrow & 990x+275x& = & 20-264 \\\Leftrightarrow & \color{red}{1265} x& = & -244 \\\Leftrightarrow & x = \frac{-244}{1265} & & \\ & V = \left\{ \frac{-244}{1265} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{9})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{8}{9}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-40} & = & \color{red}{405x} +54 \\\Leftrightarrow & 180x \color{red}{-40} \color{blue}{+40} \color{blue}{-405x} & = & \color{red}{405x} +54 \color{blue}{-405x} \color{blue}{+40} \\\Leftrightarrow & 180x-405x& = & 54+40 \\\Leftrightarrow & \color{red}{-225} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-225} & & \\\Leftrightarrow & x = \frac{-94}{225} & & \\ & V = \left\{ \frac{-94}{225} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{3})& = & 2x+\frac{2}{9} \\\Leftrightarrow & 21x+\frac{35}{3}& = & 2x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x+ \frac{105}{ \color{blue}{9} })& = & (\frac{18}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{+105} & = & \color{red}{18x} +2 \\\Leftrightarrow & 189x \color{red}{+105} \color{blue}{-105} \color{blue}{-18x} & = & \color{red}{18x} +2 \color{blue}{-18x} \color{blue}{-105} \\\Leftrightarrow & 189x-18x& = & 2-105 \\\Leftrightarrow & \color{red}{171} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{171} & & \\ & V = \left\{ \frac{-103}{171} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -8x+\frac{6}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-352}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{-352x} +24 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{+352x} & = & \color{red}{-352x} +24 \color{blue}{+352x} \color{blue}{+165} \\\Leftrightarrow & 396x+352x& = & 24+165 \\\Leftrightarrow & \color{red}{748} x& = & 189 \\\Leftrightarrow & x = \frac{189}{748} & & \\ & V = \left\{ \frac{189}{748} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{3}{11})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{6}{11}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-220}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -220x \color{red}{-30} & = & \color{red}{495x} +66 \\\Leftrightarrow & -220x \color{red}{-30} \color{blue}{+30} \color{blue}{-495x} & = & \color{red}{495x} +66 \color{blue}{-495x} \color{blue}{+30} \\\Leftrightarrow & -220x-495x& = & 66+30 \\\Leftrightarrow & \color{red}{-715} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-715} & & \\\Leftrightarrow & x = \frac{-96}{715} & & \\ & V = \left\{ \frac{-96}{715} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{45}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{-275x} +45 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +45 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & -660x+275x& = & 45+132 \\\Leftrightarrow & \color{red}{-385} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-385} & & \\\Leftrightarrow & x = \frac{-177}{385} & & \\ & V = \left\{ \frac{-177}{385} \right\} & \\\end{align}\)
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