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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{20}{7}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{-220} & = & \color{red}{-231x} +70 \\\Leftrightarrow & 1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +70 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 1232x+231x& = & 70+220 \\\Leftrightarrow & \color{red}{1463} x& = & 290 \\\Leftrightarrow & x = \frac{290}{1463} & & \\ & V = \left\{ \frac{290}{1463} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{7})& = & -2x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{15}{7}& = & -2x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-14}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+15} & = & \color{red}{-14x} +8 \\\Leftrightarrow & 105x \color{red}{+15} \color{blue}{-15} \color{blue}{+14x} & = & \color{red}{-14x} +8 \color{blue}{+14x} \color{blue}{-15} \\\Leftrightarrow & 105x+14x& = & 8-15 \\\Leftrightarrow & \color{red}{119} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{119} & & \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{1}{2})& = & -2x+\frac{3}{2} \\\Leftrightarrow & 25x+\frac{5}{2}& = & -2x+\frac{3}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{50}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} })& = & (\frac{-4}{ \color{blue}{2} }x+ \frac{3}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 50x \color{red}{+5} & = & \color{red}{-4x} +3 \\\Leftrightarrow & 50x \color{red}{+5} \color{blue}{-5} \color{blue}{+4x} & = & \color{red}{-4x} +3 \color{blue}{+4x} \color{blue}{-5} \\\Leftrightarrow & 50x+4x& = & 3-5 \\\Leftrightarrow & \color{red}{54} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{54} & & \\\Leftrightarrow & x = \frac{-1}{27} & & \\ & V = \left\{ \frac{-1}{27} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -30x+\frac{24}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{216}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+216} & = & \color{red}{693x} +110 \\\Leftrightarrow & -2970x \color{red}{+216} \color{blue}{-216} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-216} \\\Leftrightarrow & -2970x-693x& = & 110-216 \\\Leftrightarrow & \color{red}{-3663} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{-3663} & & \\\Leftrightarrow & x = \frac{106}{3663} & & \\ & V = \left\{ \frac{106}{3663} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{2}{3})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -28x+\frac{14}{3}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+42} & = & \color{red}{-81x} +8 \\\Leftrightarrow & -252x \color{red}{+42} \color{blue}{-42} \color{blue}{+81x} & = & \color{red}{-81x} +8 \color{blue}{+81x} \color{blue}{-42} \\\Leftrightarrow & -252x+81x& = & 8-42 \\\Leftrightarrow & \color{red}{-171} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-171} & & \\\Leftrightarrow & x = \frac{34}{171} & & \\ & V = \left\{ \frac{34}{171} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{-110x} +99 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+36} \\\Leftrightarrow & -528x+110x& = & 99+36 \\\Leftrightarrow & \color{red}{-418} x& = & 135 \\\Leftrightarrow & x = \frac{135}{-418} & & \\\Leftrightarrow & x = \frac{-135}{418} & & \\ & V = \left\{ \frac{-135}{418} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{378}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 378x \color{red}{-36} & = & \color{red}{-105x} +28 \\\Leftrightarrow & 378x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & 378x+105x& = & 28+36 \\\Leftrightarrow & \color{red}{483} x& = & 64 \\\Leftrightarrow & x = \frac{64}{483} & & \\ & V = \left\{ \frac{64}{483} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & -126x-147x& = & 28-30 \\\Leftrightarrow & \color{red}{-273} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-273} & & \\\Leftrightarrow & x = \frac{2}{273} & & \\ & V = \left\{ \frac{2}{273} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{8})& = & 6x+\frac{3}{8} \\\Leftrightarrow & -25x+\frac{15}{8}& = & 6x+\frac{3}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{48}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{+15} & = & \color{red}{48x} +3 \\\Leftrightarrow & -200x \color{red}{+15} \color{blue}{-15} \color{blue}{-48x} & = & \color{red}{48x} +3 \color{blue}{-48x} \color{blue}{-15} \\\Leftrightarrow & -200x-48x& = & 3-15 \\\Leftrightarrow & \color{red}{-248} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-248} & & \\\Leftrightarrow & x = \frac{3}{62} & & \\ & V = \left\{ \frac{3}{62} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{11})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -30x+\frac{12}{11}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{60}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+60} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -1650x \color{red}{+60} \color{blue}{-60} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-60} \\\Leftrightarrow & -1650x+385x& = & 22-60 \\\Leftrightarrow & \color{red}{-1265} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-1265} & & \\\Leftrightarrow & x = \frac{38}{1265} & & \\ & V = \left\{ \frac{38}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-54} & = & \color{red}{231x} +110 \\\Leftrightarrow & 990x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 990x-231x& = & 110+54 \\\Leftrightarrow & \color{red}{759} x& = & 164 \\\Leftrightarrow & x = \frac{164}{759} & & \\ & V = \left\{ \frac{164}{759} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{98x} +49 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+12} \\\Leftrightarrow & -84x-98x& = & 49+12 \\\Leftrightarrow & \color{red}{-182} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-182} & & \\\Leftrightarrow & x = \frac{-61}{182} & & \\ & V = \left\{ \frac{-61}{182} \right\} & \\\end{align}\)
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