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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{11})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{8}{11}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+56} & = & \color{red}{-231x} +110 \\\Leftrightarrow & 770x \color{red}{+56} \color{blue}{-56} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{-56} \\\Leftrightarrow & 770x+231x& = & 110-56 \\\Leftrightarrow & \color{red}{1001} x& = & 54 \\\Leftrightarrow & x = \frac{54}{1001} & & \\ & V = \left\{ \frac{54}{1001} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{3}{10})& = & 2x+\frac{3}{5} \\\Leftrightarrow & 9x+\frac{9}{10}& = & 2x+\frac{3}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{90}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{6}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 90x \color{red}{+9} & = & \color{red}{20x} +6 \\\Leftrightarrow & 90x \color{red}{+9} \color{blue}{-9} \color{blue}{-20x} & = & \color{red}{20x} +6 \color{blue}{-20x} \color{blue}{-9} \\\Leftrightarrow & 90x-20x& = & 6-9 \\\Leftrightarrow & \color{red}{70} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{5}{7})& = & 3x+\frac{9}{8} \\\Leftrightarrow & 8x+\frac{10}{7}& = & 3x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{+80} & = & \color{red}{168x} +63 \\\Leftrightarrow & 448x \color{red}{+80} \color{blue}{-80} \color{blue}{-168x} & = & \color{red}{168x} +63 \color{blue}{-168x} \color{blue}{-80} \\\Leftrightarrow & 448x-168x& = & 63-80 \\\Leftrightarrow & \color{red}{280} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{280} & & \\ & V = \left\{ \frac{-17}{280} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{11})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -9x+\frac{6}{11}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+42} & = & \color{red}{-385x} +44 \\\Leftrightarrow & -693x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & -693x+385x& = & 44-42 \\\Leftrightarrow & \color{red}{-308} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-308} & & \\\Leftrightarrow & x = \frac{-1}{154} & & \\ & V = \left\{ \frac{-1}{154} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 20x+\frac{15}{4}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{-180x} +32 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{+180x} & = & \color{red}{-180x} +32 \color{blue}{+180x} \color{blue}{-75} \\\Leftrightarrow & 400x+180x& = & 32-75 \\\Leftrightarrow & \color{red}{580} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{580} & & \\ & V = \left\{ \frac{-43}{580} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{11})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 20x+\frac{10}{11}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{880}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 880x \color{red}{+40} & = & \color{red}{-132x} +99 \\\Leftrightarrow & 880x \color{red}{+40} \color{blue}{-40} \color{blue}{+132x} & = & \color{red}{-132x} +99 \color{blue}{+132x} \color{blue}{-40} \\\Leftrightarrow & 880x+132x& = & 99-40 \\\Leftrightarrow & \color{red}{1012} x& = & 59 \\\Leftrightarrow & x = \frac{59}{1012} & & \\ & V = \left\{ \frac{59}{1012} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{7})& = & 7x+\frac{5}{9} \\\Leftrightarrow & 12x+\frac{20}{7}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+180} & = & \color{red}{441x} +35 \\\Leftrightarrow & 756x \color{red}{+180} \color{blue}{-180} \color{blue}{-441x} & = & \color{red}{441x} +35 \color{blue}{-441x} \color{blue}{-180} \\\Leftrightarrow & 756x-441x& = & 35-180 \\\Leftrightarrow & \color{red}{315} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{315} & & \\\Leftrightarrow & x = \frac{-29}{63} & & \\ & V = \left\{ \frac{-29}{63} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{5}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -30x-\frac{30}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-60} & = & \color{red}{154x} +33 \\\Leftrightarrow & -660x \color{red}{-60} \color{blue}{+60} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+60} \\\Leftrightarrow & -660x-154x& = & 33+60 \\\Leftrightarrow & \color{red}{-814} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-814} & & \\\Leftrightarrow & x = \frac{-93}{814} & & \\ & V = \left\{ \frac{-93}{814} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -3x+\frac{3}{10} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -3x+\frac{3}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{12}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{-105} & = & \color{red}{-120x} +12 \\\Leftrightarrow & 1400x \color{red}{-105} \color{blue}{+105} \color{blue}{+120x} & = & \color{red}{-120x} +12 \color{blue}{+120x} \color{blue}{+105} \\\Leftrightarrow & 1400x+120x& = & 12+105 \\\Leftrightarrow & \color{red}{1520} x& = & 117 \\\Leftrightarrow & x = \frac{117}{1520} & & \\ & V = \left\{ \frac{117}{1520} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{48}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-48} & = & \color{red}{231x} +88 \\\Leftrightarrow & -660x \color{red}{-48} \color{blue}{+48} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+48} \\\Leftrightarrow & -660x-231x& = & 88+48 \\\Leftrightarrow & \color{red}{-891} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-891} & & \\\Leftrightarrow & x = \frac{-136}{891} & & \\ & V = \left\{ \frac{-136}{891} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{175x} +56 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{+150} \\\Leftrightarrow & -840x-175x& = & 56+150 \\\Leftrightarrow & \color{red}{-1015} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-1015} & & \\\Leftrightarrow & x = \frac{-206}{1015} & & \\ & V = \left\{ \frac{-206}{1015} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{4})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{140}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -252x \color{red}{-105} & = & \color{red}{140x} +16 \\\Leftrightarrow & -252x \color{red}{-105} \color{blue}{+105} \color{blue}{-140x} & = & \color{red}{140x} +16 \color{blue}{-140x} \color{blue}{+105} \\\Leftrightarrow & -252x-140x& = & 16+105 \\\Leftrightarrow & \color{red}{-392} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-392} & & \\\Leftrightarrow & x = \frac{-121}{392} & & \\ & V = \left\{ \frac{-121}{392} \right\} & \\\end{align}\)
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