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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 21x+\frac{14}{3}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{98}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+98} & = & \color{red}{-105x} +24 \\\Leftrightarrow & 441x \color{red}{+98} \color{blue}{-98} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{-98} \\\Leftrightarrow & 441x+105x& = & 24-98 \\\Leftrightarrow & \color{red}{546} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{546} & & \\\Leftrightarrow & x = \frac{-37}{273} & & \\ & V = \left\{ \frac{-37}{273} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & 5x+\frac{9}{8} \\\Leftrightarrow & 18x+\frac{12}{5}& = & 5x+\frac{9}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{720}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{45}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 720x \color{red}{+96} & = & \color{red}{200x} +45 \\\Leftrightarrow & 720x \color{red}{+96} \color{blue}{-96} \color{blue}{-200x} & = & \color{red}{200x} +45 \color{blue}{-200x} \color{blue}{-96} \\\Leftrightarrow & 720x-200x& = & 45-96 \\\Leftrightarrow & \color{red}{520} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{520} & & \\ & V = \left\{ \frac{-51}{520} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x+\frac{16}{7}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-560}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{245x} +42 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{-245x} & = & \color{red}{245x} +42 \color{blue}{-245x} \color{blue}{-80} \\\Leftrightarrow & -560x-245x& = & 42-80 \\\Leftrightarrow & \color{red}{-805} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-805} & & \\\Leftrightarrow & x = \frac{38}{805} & & \\ & V = \left\{ \frac{38}{805} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{891x} +72 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{-891x} & = & \color{red}{891x} +72 \color{blue}{-891x} \color{blue}{-88} \\\Leftrightarrow & -792x-891x& = & 72-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1683} & & \\\Leftrightarrow & x = \frac{16}{1683} & & \\ & V = \left\{ \frac{16}{1683} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{385x} +44 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -924x-385x& = & 44-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-1309} & & \\\Leftrightarrow & x = \frac{82}{1309} & & \\ & V = \left\{ \frac{82}{1309} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -24x+\frac{24}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1080}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1080x \color{red}{+216} & = & \color{red}{225x} +40 \\\Leftrightarrow & -1080x \color{red}{+216} \color{blue}{-216} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{-216} \\\Leftrightarrow & -1080x-225x& = & 40-216 \\\Leftrightarrow & \color{red}{-1305} x& = & -176 \\\Leftrightarrow & x = \frac{-176}{-1305} & & \\\Leftrightarrow & x = \frac{176}{1305} & & \\ & V = \left\{ \frac{176}{1305} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{4})& = & 2x+\frac{10}{9} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 2x+\frac{10}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{540}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{72}{ \color{blue}{36} }x+ \frac{40}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 540x \color{red}{+135} & = & \color{red}{72x} +40 \\\Leftrightarrow & 540x \color{red}{+135} \color{blue}{-135} \color{blue}{-72x} & = & \color{red}{72x} +40 \color{blue}{-72x} \color{blue}{-135} \\\Leftrightarrow & 540x-72x& = & 40-135 \\\Leftrightarrow & \color{red}{468} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{468} & & \\ & V = \left\{ \frac{-95}{468} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{11})& = & 8x+\frac{8}{3} \\\Leftrightarrow & -28x-\frac{35}{11}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-105} & = & \color{red}{264x} +88 \\\Leftrightarrow & -924x \color{red}{-105} \color{blue}{+105} \color{blue}{-264x} & = & \color{red}{264x} +88 \color{blue}{-264x} \color{blue}{+105} \\\Leftrightarrow & -924x-264x& = & 88+105 \\\Leftrightarrow & \color{red}{-1188} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-1188} & & \\\Leftrightarrow & x = \frac{-193}{1188} & & \\ & V = \left\{ \frac{-193}{1188} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{12}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-84} & = & \color{red}{539x} +44 \\\Leftrightarrow & -1232x \color{red}{-84} \color{blue}{+84} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{+84} \\\Leftrightarrow & -1232x-539x& = & 44+84 \\\Leftrightarrow & \color{red}{-1771} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-1771} & & \\\Leftrightarrow & x = \frac{-128}{1771} & & \\ & V = \left\{ \frac{-128}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +20 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +20 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 20+36 \\\Leftrightarrow & \color{red}{-255} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-255} & & \\\Leftrightarrow & x = \frac{-56}{255} & & \\ & V = \left\{ \frac{-56}{255} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{4})& = & -9x+\frac{8}{7} \\\Leftrightarrow & 28x+\frac{35}{4}& = & -9x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{784}{ \color{blue}{28} }x+ \frac{245}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 784x \color{red}{+245} & = & \color{red}{-252x} +32 \\\Leftrightarrow & 784x \color{red}{+245} \color{blue}{-245} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{-245} \\\Leftrightarrow & 784x+252x& = & 32-245 \\\Leftrightarrow & \color{red}{1036} x& = & -213 \\\Leftrightarrow & x = \frac{-213}{1036} & & \\ & V = \left\{ \frac{-213}{1036} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{5})& = & 6x+\frac{5}{2} \\\Leftrightarrow & -18x-\frac{24}{5}& = & 6x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{60}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{60x} +25 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{+48} \\\Leftrightarrow & -180x-60x& = & 25+48 \\\Leftrightarrow & \color{red}{-240} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-240} & & \\\Leftrightarrow & x = \frac{-73}{240} & & \\ & V = \left\{ \frac{-73}{240} \right\} & \\\end{align}\)
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