Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x+\frac{4}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+12} & = & \color{red}{75x} +50 \\\Leftrightarrow & 90x \color{red}{+12} \color{blue}{-12} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-12} \\\Leftrightarrow & 90x-75x& = & 50-12 \\\Leftrightarrow & \color{red}{15} x& = & 38 \\\Leftrightarrow & x = \frac{38}{15} & & \\ & V = \left\{ \frac{38}{15} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{4}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{20}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-630}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -630x \color{red}{-180} & = & \color{red}{-441x} +28 \\\Leftrightarrow & -630x \color{red}{-180} \color{blue}{+180} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{+180} \\\Leftrightarrow & -630x+441x& = & 28+180 \\\Leftrightarrow & \color{red}{-189} x& = & 208 \\\Leftrightarrow & x = \frac{208}{-189} & & \\\Leftrightarrow & x = \frac{-208}{189} & & \\ & V = \left\{ \frac{-208}{189} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{3}{7})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 8x-\frac{6}{7}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-66} & = & \color{red}{-693x} +70 \\\Leftrightarrow & 616x \color{red}{-66} \color{blue}{+66} \color{blue}{+693x} & = & \color{red}{-693x} +70 \color{blue}{+693x} \color{blue}{+66} \\\Leftrightarrow & 616x+693x& = & 70+66 \\\Leftrightarrow & \color{red}{1309} x& = & 136 \\\Leftrightarrow & x = \frac{136}{1309} & & \\\Leftrightarrow & x = \frac{8}{77} & & \\ & V = \left\{ \frac{8}{77} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-12}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -12x \color{red}{+10} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -12x \color{red}{+10} \color{blue}{-10} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{-10} \\\Leftrightarrow & -12x+15x& = & 4-10 \\\Leftrightarrow & \color{red}{3} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{3} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{-8} & = & \color{red}{-21x} +2 \\\Leftrightarrow & 18x \color{red}{-8} \color{blue}{+8} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+8} \\\Leftrightarrow & 18x+21x& = & 2+8 \\\Leftrightarrow & \color{red}{39} x& = & 10 \\\Leftrightarrow & x = \frac{10}{39} & & \\ & V = \left\{ \frac{10}{39} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{25}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x+ \frac{250}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{+250} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -1100x \color{red}{+250} \color{blue}{-250} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{-250} \\\Leftrightarrow & -1100x+770x& = & 33-250 \\\Leftrightarrow & \color{red}{-330} x& = & -217 \\\Leftrightarrow & x = \frac{-217}{-330} & & \\\Leftrightarrow & x = \frac{217}{330} & & \\ & V = \left\{ \frac{217}{330} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{3}{2})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{9}{2}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{27}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-27} & = & \color{red}{-42x} +20 \\\Leftrightarrow & 90x \color{red}{-27} \color{blue}{+27} \color{blue}{+42x} & = & \color{red}{-42x} +20 \color{blue}{+42x} \color{blue}{+27} \\\Leftrightarrow & 90x+42x& = & 20+27 \\\Leftrightarrow & \color{red}{132} x& = & 47 \\\Leftrightarrow & x = \frac{47}{132} & & \\ & V = \left\{ \frac{47}{132} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & -4x+\frac{8}{11} \\\Leftrightarrow & -15x+\frac{15}{4}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-660}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-176}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -660x \color{red}{+165} & = & \color{red}{-176x} +32 \\\Leftrightarrow & -660x \color{red}{+165} \color{blue}{-165} \color{blue}{+176x} & = & \color{red}{-176x} +32 \color{blue}{+176x} \color{blue}{-165} \\\Leftrightarrow & -660x+176x& = & 32-165 \\\Leftrightarrow & \color{red}{-484} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-484} & & \\\Leftrightarrow & x = \frac{133}{484} & & \\ & V = \left\{ \frac{133}{484} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -8x+\frac{5}{8} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -8x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{112}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+112} & = & \color{red}{-192x} +15 \\\Leftrightarrow & 504x \color{red}{+112} \color{blue}{-112} \color{blue}{+192x} & = & \color{red}{-192x} +15 \color{blue}{+192x} \color{blue}{-112} \\\Leftrightarrow & 504x+192x& = & 15-112 \\\Leftrightarrow & \color{red}{696} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{696} & & \\ & V = \left\{ \frac{-97}{696} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{2}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x+\frac{4}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{70x} +15 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-8} \\\Leftrightarrow & -60x-70x& = & 15-8 \\\Leftrightarrow & \color{red}{-130} x& = & 7 \\\Leftrightarrow & x = \frac{7}{-130} & & \\\Leftrightarrow & x = \frac{-7}{130} & & \\ & V = \left\{ \frac{-7}{130} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{2}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{-15x} +2 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{+15x} & = & \color{red}{-15x} +2 \color{blue}{+15x} \color{blue}{+12} \\\Leftrightarrow & -100x+15x& = & 2+12 \\\Leftrightarrow & \color{red}{-85} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-85} & & \\\Leftrightarrow & x = \frac{-14}{85} & & \\ & V = \left\{ \frac{-14}{85} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 10x-\frac{25}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{275}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-275} & = & \color{red}{539x} +35 \\\Leftrightarrow & 770x \color{red}{-275} \color{blue}{+275} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+275} \\\Leftrightarrow & 770x-539x& = & 35+275 \\\Leftrightarrow & \color{red}{231} x& = & 310 \\\Leftrightarrow & x = \frac{310}{231} & & \\ & V = \left\{ \frac{310}{231} \right\} & \\\end{align}\)
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