Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{-315x} +10 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{-36} \\\Leftrightarrow & -270x+315x& = & 10-36 \\\Leftrightarrow & \color{red}{45} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{45} & & \\ & V = \left\{ \frac{-26}{45} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{35x} +6 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +6 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 150x-35x& = & 6+12 \\\Leftrightarrow & \color{red}{115} x& = & 18 \\\Leftrightarrow & x = \frac{18}{115} & & \\ & V = \left\{ \frac{18}{115} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+28} & = & \color{red}{-9x} +8 \\\Leftrightarrow & 84x \color{red}{+28} \color{blue}{-28} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{-28} \\\Leftrightarrow & 84x+9x& = & 8-28 \\\Leftrightarrow & \color{red}{93} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{93} & & \\ & V = \left\{ \frac{-20}{93} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-132} & = & \color{red}{165x} +25 \\\Leftrightarrow & -1100x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +25 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & -1100x-165x& = & 25+132 \\\Leftrightarrow & \color{red}{-1265} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-1265} & & \\\Leftrightarrow & x = \frac{-157}{1265} & & \\ & V = \left\{ \frac{-157}{1265} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{9})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -21x-\frac{28}{9}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-756}{ \color{blue}{36} }x- \frac{112}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -756x \color{red}{-112} & = & \color{red}{288x} +27 \\\Leftrightarrow & -756x \color{red}{-112} \color{blue}{+112} \color{blue}{-288x} & = & \color{red}{288x} +27 \color{blue}{-288x} \color{blue}{+112} \\\Leftrightarrow & -756x-288x& = & 27+112 \\\Leftrightarrow & \color{red}{-1044} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-1044} & & \\\Leftrightarrow & x = \frac{-139}{1044} & & \\ & V = \left\{ \frac{-139}{1044} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -8x+\frac{2}{9} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2016}{ \color{blue}{72} }x- \frac{189}{ \color{blue}{72} })& = & (\frac{-576}{ \color{blue}{72} }x+ \frac{16}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2016x \color{red}{-189} & = & \color{red}{-576x} +16 \\\Leftrightarrow & -2016x \color{red}{-189} \color{blue}{+189} \color{blue}{+576x} & = & \color{red}{-576x} +16 \color{blue}{+576x} \color{blue}{+189} \\\Leftrightarrow & -2016x+576x& = & 16+189 \\\Leftrightarrow & \color{red}{-1440} x& = & 205 \\\Leftrightarrow & x = \frac{205}{-1440} & & \\\Leftrightarrow & x = \frac{-41}{288} & & \\ & V = \left\{ \frac{-41}{288} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{7})& = & -7x+\frac{5}{3} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{-147x} +35 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +35 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & 630x+147x& = & 35-90 \\\Leftrightarrow & \color{red}{777} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{777} & & \\ & V = \left\{ \frac{-55}{777} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -4x+\frac{7}{11} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -4x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+99} & = & \color{red}{-220x} +35 \\\Leftrightarrow & 825x \color{red}{+99} \color{blue}{-99} \color{blue}{+220x} & = & \color{red}{-220x} +35 \color{blue}{+220x} \color{blue}{-99} \\\Leftrightarrow & 825x+220x& = & 35-99 \\\Leftrightarrow & \color{red}{1045} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{1045} & & \\ & V = \left\{ \frac{-64}{1045} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{99}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-99} & = & \color{red}{-385x} +30 \\\Leftrightarrow & 660x \color{red}{-99} \color{blue}{+99} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+99} \\\Leftrightarrow & 660x+385x& = & 30+99 \\\Leftrightarrow & \color{red}{1045} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1045} & & \\ & V = \left\{ \frac{129}{1045} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{11})& = & -6x+\frac{4}{7} \\\Leftrightarrow & -35x+\frac{28}{11}& = & -6x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2695}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2695x \color{red}{+196} & = & \color{red}{-462x} +44 \\\Leftrightarrow & -2695x \color{red}{+196} \color{blue}{-196} \color{blue}{+462x} & = & \color{red}{-462x} +44 \color{blue}{+462x} \color{blue}{-196} \\\Leftrightarrow & -2695x+462x& = & 44-196 \\\Leftrightarrow & \color{red}{-2233} x& = & -152 \\\Leftrightarrow & x = \frac{-152}{-2233} & & \\\Leftrightarrow & x = \frac{152}{2233} & & \\ & V = \left\{ \frac{152}{2233} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & 2x+\frac{9}{5} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 2x+\frac{9}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{80}{ \color{blue}{40} }x+ \frac{72}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+75} & = & \color{red}{80x} +72 \\\Leftrightarrow & 600x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +72 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & 600x-80x& = & 72-75 \\\Leftrightarrow & \color{red}{520} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{520} & & \\ & V = \left\{ \frac{-3}{520} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{6}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-18} & = & \color{red}{105x} +20 \\\Leftrightarrow & 180x \color{red}{-18} \color{blue}{+18} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+18} \\\Leftrightarrow & 180x-105x& = & 20+18 \\\Leftrightarrow & \color{red}{75} x& = & 38 \\\Leftrightarrow & x = \frac{38}{75} & & \\ & V = \left\{ \frac{38}{75} \right\} & \\\end{align}\)
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