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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{11})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -21x+\frac{35}{11}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1617}{ \color{blue}{77} }x+ \frac{245}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1617x \color{red}{+245} & = & \color{red}{-616x} +110 \\\Leftrightarrow & -1617x \color{red}{+245} \color{blue}{-245} \color{blue}{+616x} & = & \color{red}{-616x} +110 \color{blue}{+616x} \color{blue}{-245} \\\Leftrightarrow & -1617x+616x& = & 110-245 \\\Leftrightarrow & \color{red}{-1001} x& = & -135 \\\Leftrightarrow & x = \frac{-135}{-1001} & & \\\Leftrightarrow & x = \frac{135}{1001} & & \\ & V = \left\{ \frac{135}{1001} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{8}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{56}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-56} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -420x \color{red}{-56} \color{blue}{+56} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+56} \\\Leftrightarrow & -420x+175x& = & 50+56 \\\Leftrightarrow & \color{red}{-245} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-245} & & \\\Leftrightarrow & x = \frac{-106}{245} & & \\ & V = \left\{ \frac{-106}{245} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{7})& = & -7x+\frac{5}{12} \\\Leftrightarrow & -30x-\frac{30}{7}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-2520}{ \color{blue}{84} }x- \frac{360}{ \color{blue}{84} })& = & (\frac{-588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -2520x \color{red}{-360} & = & \color{red}{-588x} +35 \\\Leftrightarrow & -2520x \color{red}{-360} \color{blue}{+360} \color{blue}{+588x} & = & \color{red}{-588x} +35 \color{blue}{+588x} \color{blue}{+360} \\\Leftrightarrow & -2520x+588x& = & 35+360 \\\Leftrightarrow & \color{red}{-1932} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-1932} & & \\\Leftrightarrow & x = \frac{-395}{1932} & & \\ & V = \left\{ \frac{-395}{1932} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{2})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -25x-\frac{25}{2}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-250}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -250x \color{red}{-125} & = & \color{red}{-80x} +16 \\\Leftrightarrow & -250x \color{red}{-125} \color{blue}{+125} \color{blue}{+80x} & = & \color{red}{-80x} +16 \color{blue}{+80x} \color{blue}{+125} \\\Leftrightarrow & -250x+80x& = & 16+125 \\\Leftrightarrow & \color{red}{-170} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-170} & & \\\Leftrightarrow & x = \frac{-141}{170} & & \\ & V = \left\{ \frac{-141}{170} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -20x-\frac{10}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-70} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -1540x \color{red}{-70} \color{blue}{+70} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{+70} \\\Leftrightarrow & -1540x+539x& = & 110+70 \\\Leftrightarrow & \color{red}{-1001} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-1001} & & \\\Leftrightarrow & x = \frac{-180}{1001} & & \\ & V = \left\{ \frac{-180}{1001} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{105x} +42 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-105x} & = & \color{red}{105x} +42 \color{blue}{-105x} \color{blue}{+100} \\\Leftrightarrow & 700x-105x& = & 42+100 \\\Leftrightarrow & \color{red}{595} x& = & 142 \\\Leftrightarrow & x = \frac{142}{595} & & \\ & V = \left\{ \frac{142}{595} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{-175x} +45 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{+175x} & = & \color{red}{-175x} +45 \color{blue}{+175x} \color{blue}{-84} \\\Leftrightarrow & 630x+175x& = & 45-84 \\\Leftrightarrow & \color{red}{805} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{805} & & \\ & V = \left\{ \frac{-39}{805} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -9x-\frac{9}{10}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 10 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-180}{ \color{blue}{20} }x- \frac{18}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -180x \color{red}{-18} & = & \color{red}{-100x} +15 \\\Leftrightarrow & -180x \color{red}{-18} \color{blue}{+18} \color{blue}{+100x} & = & \color{red}{-100x} +15 \color{blue}{+100x} \color{blue}{+18} \\\Leftrightarrow & -180x+100x& = & 15+18 \\\Leftrightarrow & \color{red}{-80} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-80} & & \\\Leftrightarrow & x = \frac{-33}{80} & & \\ & V = \left\{ \frac{-33}{80} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+330} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -2310x \color{red}{+330} \color{blue}{-330} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-330} \\\Leftrightarrow & -2310x+539x& = & 42-330 \\\Leftrightarrow & \color{red}{-1771} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{-1771} & & \\\Leftrightarrow & x = \frac{288}{1771} & & \\ & V = \left\{ \frac{288}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-220} & = & \color{red}{539x} +28 \\\Leftrightarrow & 1540x \color{red}{-220} \color{blue}{+220} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{+220} \\\Leftrightarrow & 1540x-539x& = & 28+220 \\\Leftrightarrow & \color{red}{1001} x& = & 248 \\\Leftrightarrow & x = \frac{248}{1001} & & \\ & V = \left\{ \frac{248}{1001} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{4})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x+\frac{15}{4}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+165} & = & \color{red}{220x} +24 \\\Leftrightarrow & 528x \color{red}{+165} \color{blue}{-165} \color{blue}{-220x} & = & \color{red}{220x} +24 \color{blue}{-220x} \color{blue}{-165} \\\Leftrightarrow & 528x-220x& = & 24-165 \\\Leftrightarrow & \color{red}{308} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{308} & & \\ & V = \left\{ \frac{-141}{308} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{11})& = & 8x+\frac{3}{11} \\\Leftrightarrow & -15x+\frac{9}{11}& = & 8x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} })& = & (\frac{88}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{+9} & = & \color{red}{88x} +3 \\\Leftrightarrow & -165x \color{red}{+9} \color{blue}{-9} \color{blue}{-88x} & = & \color{red}{88x} +3 \color{blue}{-88x} \color{blue}{-9} \\\Leftrightarrow & -165x-88x& = & 3-9 \\\Leftrightarrow & \color{red}{-253} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-253} & & \\\Leftrightarrow & x = \frac{6}{253} & & \\ & V = \left\{ \frac{6}{253} \right\} & \\\end{align}\)
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