Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{63x} +12 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{-140} \\\Leftrightarrow & -168x-63x& = & 12-140 \\\Leftrightarrow & \color{red}{-231} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-231} & & \\\Leftrightarrow & x = \frac{128}{231} & & \\ & V = \left\{ \frac{128}{231} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{135x} +10 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +10 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & 120x-135x& = & 10-36 \\\Leftrightarrow & \color{red}{-15} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-15} & & \\\Leftrightarrow & x = \frac{26}{15} & & \\ & V = \left\{ \frac{26}{15} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -12x+\frac{18}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x+ \frac{18}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{35x} +8 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{-18} \\\Leftrightarrow & -84x-35x& = & 8-18 \\\Leftrightarrow & \color{red}{-119} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-119} & & \\\Leftrightarrow & x = \frac{10}{119} & & \\ & V = \left\{ \frac{10}{119} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{11})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -30x+\frac{30}{11}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{210}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+210} & = & \color{red}{539x} +99 \\\Leftrightarrow & -2310x \color{red}{+210} \color{blue}{-210} \color{blue}{-539x} & = & \color{red}{539x} +99 \color{blue}{-539x} \color{blue}{-210} \\\Leftrightarrow & -2310x-539x& = & 99-210 \\\Leftrightarrow & \color{red}{-2849} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{-2849} & & \\\Leftrightarrow & x = \frac{3}{77} & & \\ & V = \left\{ \frac{3}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{24}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-72} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -450x \color{red}{-72} \color{blue}{+72} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+72} \\\Leftrightarrow & -450x+105x& = & 20+72 \\\Leftrightarrow & \color{red}{-345} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-345} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x+\frac{20}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+20} & = & \color{red}{45x} +6 \\\Leftrightarrow & -108x \color{red}{+20} \color{blue}{-20} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-20} \\\Leftrightarrow & -108x-45x& = & 6-20 \\\Leftrightarrow & \color{red}{-153} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-153} & & \\\Leftrightarrow & x = \frac{14}{153} & & \\ & V = \left\{ \frac{14}{153} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{5})& = & 9x+\frac{9}{7} \\\Leftrightarrow & -28x-\frac{14}{5}& = & 9x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x- \frac{98}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{-98} & = & \color{red}{315x} +45 \\\Leftrightarrow & -980x \color{red}{-98} \color{blue}{+98} \color{blue}{-315x} & = & \color{red}{315x} +45 \color{blue}{-315x} \color{blue}{+98} \\\Leftrightarrow & -980x-315x& = & 45+98 \\\Leftrightarrow & \color{red}{-1295} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-1295} & & \\\Leftrightarrow & x = \frac{-143}{1295} & & \\ & V = \left\{ \frac{-143}{1295} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+42} & = & \color{red}{-385x} +99 \\\Leftrightarrow & 462x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +99 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & 462x+385x& = & 99-42 \\\Leftrightarrow & \color{red}{847} x& = & 57 \\\Leftrightarrow & x = \frac{57}{847} & & \\ & V = \left\{ \frac{57}{847} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{7})& = & 9x+\frac{7}{5} \\\Leftrightarrow & 8x-\frac{12}{7}& = & 9x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-60} & = & \color{red}{315x} +49 \\\Leftrightarrow & 280x \color{red}{-60} \color{blue}{+60} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{+60} \\\Leftrightarrow & 280x-315x& = & 49+60 \\\Leftrightarrow & \color{red}{-35} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-35} & & \\\Leftrightarrow & x = \frac{-109}{35} & & \\ & V = \left\{ \frac{-109}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{12})& = & 6x+\frac{6}{5} \\\Leftrightarrow & -35x-\frac{35}{12}& = & 6x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-2100}{ \color{blue}{60} }x- \frac{175}{ \color{blue}{60} })& = & (\frac{360}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -2100x \color{red}{-175} & = & \color{red}{360x} +72 \\\Leftrightarrow & -2100x \color{red}{-175} \color{blue}{+175} \color{blue}{-360x} & = & \color{red}{360x} +72 \color{blue}{-360x} \color{blue}{+175} \\\Leftrightarrow & -2100x-360x& = & 72+175 \\\Leftrightarrow & \color{red}{-2460} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-2460} & & \\\Leftrightarrow & x = \frac{-247}{2460} & & \\ & V = \left\{ \frac{-247}{2460} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{10})& = & -4x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{9}{10}& = & -4x+\frac{4}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1650}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-440}{ \color{blue}{110} }x+ \frac{40}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1650x \color{red}{+99} & = & \color{red}{-440x} +40 \\\Leftrightarrow & 1650x \color{red}{+99} \color{blue}{-99} \color{blue}{+440x} & = & \color{red}{-440x} +40 \color{blue}{+440x} \color{blue}{-99} \\\Leftrightarrow & 1650x+440x& = & 40-99 \\\Leftrightarrow & \color{red}{2090} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{2090} & & \\ & V = \left\{ \frac{-59}{2090} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{+72} & = & \color{red}{-105x} +40 \\\Leftrightarrow & -450x \color{red}{+72} \color{blue}{-72} \color{blue}{+105x} & = & \color{red}{-105x} +40 \color{blue}{+105x} \color{blue}{-72} \\\Leftrightarrow & -450x+105x& = & 40-72 \\\Leftrightarrow & \color{red}{-345} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-345} & & \\\Leftrightarrow & x = \frac{32}{345} & & \\ & V = \left\{ \frac{32}{345} \right\} & \\\end{align}\)
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