Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{+264} & = & \color{red}{385x} +50 \\\Leftrightarrow & -1650x \color{red}{+264} \color{blue}{-264} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{-264} \\\Leftrightarrow & -1650x-385x& = & 50-264 \\\Leftrightarrow & \color{red}{-2035} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-2035} & & \\\Leftrightarrow & x = \frac{214}{2035} & & \\ & V = \left\{ \frac{214}{2035} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{3}{10})& = & -8x+\frac{3}{11} \\\Leftrightarrow & 9x-\frac{9}{10}& = & -8x+\frac{3}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{990}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{30}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 990x \color{red}{-99} & = & \color{red}{-880x} +30 \\\Leftrightarrow & 990x \color{red}{-99} \color{blue}{+99} \color{blue}{+880x} & = & \color{red}{-880x} +30 \color{blue}{+880x} \color{blue}{+99} \\\Leftrightarrow & 990x+880x& = & 30+99 \\\Leftrightarrow & \color{red}{1870} x& = & 129 \\\Leftrightarrow & x = \frac{129}{1870} & & \\ & V = \left\{ \frac{129}{1870} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{5}{9})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -25x-\frac{25}{9}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x- \frac{50}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{-50} & = & \color{red}{90x} +27 \\\Leftrightarrow & -450x \color{red}{-50} \color{blue}{+50} \color{blue}{-90x} & = & \color{red}{90x} +27 \color{blue}{-90x} \color{blue}{+50} \\\Leftrightarrow & -450x-90x& = & 27+50 \\\Leftrightarrow & \color{red}{-540} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-540} & & \\\Leftrightarrow & x = \frac{-77}{540} & & \\ & V = \left\{ \frac{-77}{540} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{11})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{21}{11}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{42}{ \color{blue}{22} })& = & (\frac{176}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-42} & = & \color{red}{176x} +55 \\\Leftrightarrow & -462x \color{red}{-42} \color{blue}{+42} \color{blue}{-176x} & = & \color{red}{176x} +55 \color{blue}{-176x} \color{blue}{+42} \\\Leftrightarrow & -462x-176x& = & 55+42 \\\Leftrightarrow & \color{red}{-638} x& = & 97 \\\Leftrightarrow & x = \frac{97}{-638} & & \\\Leftrightarrow & x = \frac{-97}{638} & & \\ & V = \left\{ \frac{-97}{638} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{25}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{75}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-75} & = & \color{red}{-147x} +14 \\\Leftrightarrow & -210x \color{red}{-75} \color{blue}{+75} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{+75} \\\Leftrightarrow & -210x+147x& = & 14+75 \\\Leftrightarrow & \color{red}{-63} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-63} & & \\\Leftrightarrow & x = \frac{-89}{63} & & \\ & V = \left\{ \frac{-89}{63} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -10x-\frac{15}{8}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-240}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -240x \color{red}{-45} & = & \color{red}{168x} +64 \\\Leftrightarrow & -240x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +64 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & -240x-168x& = & 64+45 \\\Leftrightarrow & \color{red}{-408} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-408} & & \\\Leftrightarrow & x = \frac{-109}{408} & & \\ & V = \left\{ \frac{-109}{408} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{5}{8})& = & 7x+\frac{8}{9} \\\Leftrightarrow & 6x+\frac{15}{8}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{432}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{504}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 432x \color{red}{+135} & = & \color{red}{504x} +64 \\\Leftrightarrow & 432x \color{red}{+135} \color{blue}{-135} \color{blue}{-504x} & = & \color{red}{504x} +64 \color{blue}{-504x} \color{blue}{-135} \\\Leftrightarrow & 432x-504x& = & 64-135 \\\Leftrightarrow & \color{red}{-72} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{-72} & & \\\Leftrightarrow & x = \frac{71}{72} & & \\ & V = \left\{ \frac{71}{72} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -12x-\frac{16}{7}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-16} & = & \color{red}{-35x} +4 \\\Leftrightarrow & -84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +4 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & -84x+35x& = & 4+16 \\\Leftrightarrow & \color{red}{-49} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-49} & & \\\Leftrightarrow & x = \frac{-20}{49} & & \\ & V = \left\{ \frac{-20}{49} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{7})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{6}{7}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+18} & = & \color{red}{105x} +70 \\\Leftrightarrow & -252x \color{red}{+18} \color{blue}{-18} \color{blue}{-105x} & = & \color{red}{105x} +70 \color{blue}{-105x} \color{blue}{-18} \\\Leftrightarrow & -252x-105x& = & 70-18 \\\Leftrightarrow & \color{red}{-357} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-357} & & \\\Leftrightarrow & x = \frac{-52}{357} & & \\ & V = \left\{ \frac{-52}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 3x+\frac{7}{9} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{-36} & = & \color{red}{135x} +35 \\\Leftrightarrow & 360x \color{red}{-36} \color{blue}{+36} \color{blue}{-135x} & = & \color{red}{135x} +35 \color{blue}{-135x} \color{blue}{+36} \\\Leftrightarrow & 360x-135x& = & 35+36 \\\Leftrightarrow & \color{red}{225} x& = & 71 \\\Leftrightarrow & x = \frac{71}{225} & & \\ & V = \left\{ \frac{71}{225} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{10}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-10} & = & \color{red}{21x} +4 \\\Leftrightarrow & -30x \color{red}{-10} \color{blue}{+10} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+10} \\\Leftrightarrow & -30x-21x& = & 4+10 \\\Leftrightarrow & \color{red}{-51} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-51} & & \\\Leftrightarrow & x = \frac{-14}{51} & & \\ & V = \left\{ \frac{-14}{51} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{7})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -16x-\frac{12}{7}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-132} & = & \color{red}{539x} +28 \\\Leftrightarrow & -1232x \color{red}{-132} \color{blue}{+132} \color{blue}{-539x} & = & \color{red}{539x} +28 \color{blue}{-539x} \color{blue}{+132} \\\Leftrightarrow & -1232x-539x& = & 28+132 \\\Leftrightarrow & \color{red}{-1771} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-1771} & & \\\Leftrightarrow & x = \frac{-160}{1771} & & \\ & V = \left\{ \frac{-160}{1771} \right\} & \\\end{align}\)
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