Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & 7x+\frac{5}{6} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{360}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{15}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 360x \color{red}{-16} & = & \color{red}{126x} +15 \\\Leftrightarrow & 360x \color{red}{-16} \color{blue}{+16} \color{blue}{-126x} & = & \color{red}{126x} +15 \color{blue}{-126x} \color{blue}{+16} \\\Leftrightarrow & 360x-126x& = & 15+16 \\\Leftrightarrow & \color{red}{234} x& = & 31 \\\Leftrightarrow & x = \frac{31}{234} & & \\ & V = \left\{ \frac{31}{234} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{3}{7} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{-245x} +15 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{+245x} & = & \color{red}{-245x} +15 \color{blue}{+245x} \color{blue}{+28} \\\Leftrightarrow & -210x+245x& = & 15+28 \\\Leftrightarrow & \color{red}{35} x& = & 43 \\\Leftrightarrow & x = \frac{43}{35} & & \\ & V = \left\{ \frac{43}{35} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{3}{8})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 25x-\frac{15}{8}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{40}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-45} & = & \color{red}{216x} +40 \\\Leftrightarrow & 600x \color{red}{-45} \color{blue}{+45} \color{blue}{-216x} & = & \color{red}{216x} +40 \color{blue}{-216x} \color{blue}{+45} \\\Leftrightarrow & 600x-216x& = & 40+45 \\\Leftrightarrow & \color{red}{384} x& = & 85 \\\Leftrightarrow & x = \frac{85}{384} & & \\ & V = \left\{ \frac{85}{384} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-330} & = & \color{red}{-539x} +56 \\\Leftrightarrow & -2310x \color{red}{-330} \color{blue}{+330} \color{blue}{+539x} & = & \color{red}{-539x} +56 \color{blue}{+539x} \color{blue}{+330} \\\Leftrightarrow & -2310x+539x& = & 56+330 \\\Leftrightarrow & \color{red}{-1771} x& = & 386 \\\Leftrightarrow & x = \frac{386}{-1771} & & \\\Leftrightarrow & x = \frac{-386}{1771} & & \\ & V = \left\{ \frac{-386}{1771} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+30} & = & \color{red}{385x} +88 \\\Leftrightarrow & 550x \color{red}{+30} \color{blue}{-30} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{-30} \\\Leftrightarrow & 550x-385x& = & 88-30 \\\Leftrightarrow & \color{red}{165} x& = & 58 \\\Leftrightarrow & x = \frac{58}{165} & & \\ & V = \left\{ \frac{58}{165} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{8})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{35}{8}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{2464}{ \color{blue}{88} }x- \frac{385}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 2464x \color{red}{-385} & = & \color{red}{-792x} +48 \\\Leftrightarrow & 2464x \color{red}{-385} \color{blue}{+385} \color{blue}{+792x} & = & \color{red}{-792x} +48 \color{blue}{+792x} \color{blue}{+385} \\\Leftrightarrow & 2464x+792x& = & 48+385 \\\Leftrightarrow & \color{red}{3256} x& = & 433 \\\Leftrightarrow & x = \frac{433}{3256} & & \\ & V = \left\{ \frac{433}{3256} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{11})& = & -5x+\frac{2}{5} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-90} & = & \color{red}{-275x} +22 \\\Leftrightarrow & 1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+275x} & = & \color{red}{-275x} +22 \color{blue}{+275x} \color{blue}{+90} \\\Leftrightarrow & 1320x+275x& = & 22+90 \\\Leftrightarrow & \color{red}{1595} x& = & 112 \\\Leftrightarrow & x = \frac{112}{1595} & & \\ & V = \left\{ \frac{112}{1595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -315x+175x& = & 20+84 \\\Leftrightarrow & \color{red}{-140} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-140} & & \\\Leftrightarrow & x = \frac{-26}{35} & & \\ & V = \left\{ \frac{-26}{35} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -180x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -180x+63x& = & 30+8 \\\Leftrightarrow & \color{red}{-117} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-117} & & \\\Leftrightarrow & x = \frac{-38}{117} & & \\ & V = \left\{ \frac{-38}{117} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{792}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 792x \color{red}{+96} & = & \color{red}{220x} +99 \\\Leftrightarrow & 792x \color{red}{+96} \color{blue}{-96} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-96} \\\Leftrightarrow & 792x-220x& = & 99-96 \\\Leftrightarrow & \color{red}{572} x& = & 3 \\\Leftrightarrow & x = \frac{3}{572} & & \\ & V = \left\{ \frac{3}{572} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-84} & = & \color{red}{315x} +50 \\\Leftrightarrow & 560x \color{red}{-84} \color{blue}{+84} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{+84} \\\Leftrightarrow & 560x-315x& = & 50+84 \\\Leftrightarrow & \color{red}{245} x& = & 134 \\\Leftrightarrow & x = \frac{134}{245} & & \\ & V = \left\{ \frac{134}{245} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & 4x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 4x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{+66} & = & \color{red}{308x} +35 \\\Leftrightarrow & 1155x \color{red}{+66} \color{blue}{-66} \color{blue}{-308x} & = & \color{red}{308x} +35 \color{blue}{-308x} \color{blue}{-66} \\\Leftrightarrow & 1155x-308x& = & 35-66 \\\Leftrightarrow & \color{red}{847} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{847} & & \\ & V = \left\{ \frac{-31}{847} \right\} & \\\end{align}\)
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