Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & 9x+\frac{4}{11} \\\Leftrightarrow & 16x-\frac{12}{5}& = & 9x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{880}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 880x \color{red}{-132} & = & \color{red}{495x} +20 \\\Leftrightarrow & 880x \color{red}{-132} \color{blue}{+132} \color{blue}{-495x} & = & \color{red}{495x} +20 \color{blue}{-495x} \color{blue}{+132} \\\Leftrightarrow & 880x-495x& = & 20+132 \\\Leftrightarrow & \color{red}{385} x& = & 152 \\\Leftrightarrow & x = \frac{152}{385} & & \\ & V = \left\{ \frac{152}{385} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{4})& = & -3x+\frac{2}{11} \\\Leftrightarrow & 10x-\frac{15}{4}& = & -3x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-165} & = & \color{red}{-132x} +8 \\\Leftrightarrow & 440x \color{red}{-165} \color{blue}{+165} \color{blue}{+132x} & = & \color{red}{-132x} +8 \color{blue}{+132x} \color{blue}{+165} \\\Leftrightarrow & 440x+132x& = & 8+165 \\\Leftrightarrow & \color{red}{572} x& = & 173 \\\Leftrightarrow & x = \frac{173}{572} & & \\ & V = \left\{ \frac{173}{572} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{3}{11})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{9}{11}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{660}{ \color{blue}{110} }x- \frac{90}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 660x \color{red}{-90} & = & \color{red}{-550x} +33 \\\Leftrightarrow & 660x \color{red}{-90} \color{blue}{+90} \color{blue}{+550x} & = & \color{red}{-550x} +33 \color{blue}{+550x} \color{blue}{+90} \\\Leftrightarrow & 660x+550x& = & 33+90 \\\Leftrightarrow & \color{red}{1210} x& = & 123 \\\Leftrightarrow & x = \frac{123}{1210} & & \\ & V = \left\{ \frac{123}{1210} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{5}{9})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{20}{9}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+140} & = & \color{red}{-315x} +90 \\\Leftrightarrow & 756x \color{red}{+140} \color{blue}{-140} \color{blue}{+315x} & = & \color{red}{-315x} +90 \color{blue}{+315x} \color{blue}{-140} \\\Leftrightarrow & 756x+315x& = & 90-140 \\\Leftrightarrow & \color{red}{1071} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{1071} & & \\ & V = \left\{ \frac{-50}{1071} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 10x+\frac{6}{7}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 140x \color{red}{+12} & = & \color{red}{42x} +49 \\\Leftrightarrow & 140x \color{red}{+12} \color{blue}{-12} \color{blue}{-42x} & = & \color{red}{42x} +49 \color{blue}{-42x} \color{blue}{-12} \\\Leftrightarrow & 140x-42x& = & 49-12 \\\Leftrightarrow & \color{red}{98} x& = & 37 \\\Leftrightarrow & x = \frac{37}{98} & & \\ & V = \left\{ \frac{37}{98} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 8x+\frac{6}{11} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-132} & = & \color{red}{440x} +30 \\\Leftrightarrow & 825x \color{red}{-132} \color{blue}{+132} \color{blue}{-440x} & = & \color{red}{440x} +30 \color{blue}{-440x} \color{blue}{+132} \\\Leftrightarrow & 825x-440x& = & 30+132 \\\Leftrightarrow & \color{red}{385} x& = & 162 \\\Leftrightarrow & x = \frac{162}{385} & & \\ & V = \left\{ \frac{162}{385} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{-48} & = & \color{red}{-105x} +28 \\\Leftrightarrow & 252x \color{red}{-48} \color{blue}{+48} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{+48} \\\Leftrightarrow & 252x+105x& = & 28+48 \\\Leftrightarrow & \color{red}{357} x& = & 76 \\\Leftrightarrow & x = \frac{76}{357} & & \\ & V = \left\{ \frac{76}{357} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{20}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-140} & = & \color{red}{441x} +90 \\\Leftrightarrow & -1008x \color{red}{-140} \color{blue}{+140} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{+140} \\\Leftrightarrow & -1008x-441x& = & 90+140 \\\Leftrightarrow & \color{red}{-1449} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1449} & & \\\Leftrightarrow & x = \frac{-10}{63} & & \\ & V = \left\{ \frac{-10}{63} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{11})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{8}{11}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+56} & = & \color{red}{693x} +44 \\\Leftrightarrow & -1540x \color{red}{+56} \color{blue}{-56} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{-56} \\\Leftrightarrow & -1540x-693x& = & 44-56 \\\Leftrightarrow & \color{red}{-2233} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-2233} & & \\\Leftrightarrow & x = \frac{12}{2233} & & \\ & V = \left\{ \frac{12}{2233} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & 270x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{375} x& = & 56 \\\Leftrightarrow & x = \frac{56}{375} & & \\ & V = \left\{ \frac{56}{375} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{11})& = & -3x+\frac{8}{11} \\\Leftrightarrow & 10x-\frac{25}{11}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x- \frac{25}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{-25} & = & \color{red}{-33x} +8 \\\Leftrightarrow & 110x \color{red}{-25} \color{blue}{+25} \color{blue}{+33x} & = & \color{red}{-33x} +8 \color{blue}{+33x} \color{blue}{+25} \\\Leftrightarrow & 110x+33x& = & 8+25 \\\Leftrightarrow & \color{red}{143} x& = & 33 \\\Leftrightarrow & x = \frac{33}{143} & & \\\Leftrightarrow & x = \frac{3}{13} & & \\ & V = \left\{ \frac{3}{13} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{9})& = & 4x+\frac{3}{10} \\\Leftrightarrow & 21x-\frac{35}{9}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1890}{ \color{blue}{90} }x- \frac{350}{ \color{blue}{90} })& = & (\frac{360}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1890x \color{red}{-350} & = & \color{red}{360x} +27 \\\Leftrightarrow & 1890x \color{red}{-350} \color{blue}{+350} \color{blue}{-360x} & = & \color{red}{360x} +27 \color{blue}{-360x} \color{blue}{+350} \\\Leftrightarrow & 1890x-360x& = & 27+350 \\\Leftrightarrow & \color{red}{1530} x& = & 377 \\\Leftrightarrow & x = \frac{377}{1530} & & \\ & V = \left\{ \frac{377}{1530} \right\} & \\\end{align}\)
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