Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & 9x+\frac{7}{8} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-320}{ \color{blue}{40} }x+ \frac{64}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -320x \color{red}{+64} & = & \color{red}{360x} +35 \\\Leftrightarrow & -320x \color{red}{+64} \color{blue}{-64} \color{blue}{-360x} & = & \color{red}{360x} +35 \color{blue}{-360x} \color{blue}{-64} \\\Leftrightarrow & -320x-360x& = & 35-64 \\\Leftrightarrow & \color{red}{-680} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{-680} & & \\\Leftrightarrow & x = \frac{29}{680} & & \\ & V = \left\{ \frac{29}{680} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{3})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -6x-\frac{4}{3}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-28} & = & \color{red}{147x} +30 \\\Leftrightarrow & -126x \color{red}{-28} \color{blue}{+28} \color{blue}{-147x} & = & \color{red}{147x} +30 \color{blue}{-147x} \color{blue}{+28} \\\Leftrightarrow & -126x-147x& = & 30+28 \\\Leftrightarrow & \color{red}{-273} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-273} & & \\\Leftrightarrow & x = \frac{-58}{273} & & \\ & V = \left\{ \frac{-58}{273} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{5}{8})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+45} & = & \color{red}{-120x} +64 \\\Leftrightarrow & 288x \color{red}{+45} \color{blue}{-45} \color{blue}{+120x} & = & \color{red}{-120x} +64 \color{blue}{+120x} \color{blue}{-45} \\\Leftrightarrow & 288x+120x& = & 64-45 \\\Leftrightarrow & \color{red}{408} x& = & 19 \\\Leftrightarrow & x = \frac{19}{408} & & \\ & V = \left\{ \frac{19}{408} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{2}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & -25x-\frac{10}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-825}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -825x \color{red}{-30} & = & \color{red}{231x} +22 \\\Leftrightarrow & -825x \color{red}{-30} \color{blue}{+30} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+30} \\\Leftrightarrow & -825x-231x& = & 22+30 \\\Leftrightarrow & \color{red}{-1056} x& = & 52 \\\Leftrightarrow & x = \frac{52}{-1056} & & \\\Leftrightarrow & x = \frac{-13}{264} & & \\ & V = \left\{ \frac{-13}{264} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & 2x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{6}{5}& = & 2x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+42} & = & \color{red}{70x} +40 \\\Leftrightarrow & 525x \color{red}{+42} \color{blue}{-42} \color{blue}{-70x} & = & \color{red}{70x} +40 \color{blue}{-70x} \color{blue}{-42} \\\Leftrightarrow & 525x-70x& = & 40-42 \\\Leftrightarrow & \color{red}{455} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{455} & & \\ & V = \left\{ \frac{-2}{455} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 15x+\frac{9}{5}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+27} & = & \color{red}{-30x} +10 \\\Leftrightarrow & 225x \color{red}{+27} \color{blue}{-27} \color{blue}{+30x} & = & \color{red}{-30x} +10 \color{blue}{+30x} \color{blue}{-27} \\\Leftrightarrow & 225x+30x& = & 10-27 \\\Leftrightarrow & \color{red}{255} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{255} & & \\\Leftrightarrow & x = \frac{-1}{15} & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-70x} +14 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+70x} & = & \color{red}{-70x} +14 \color{blue}{+70x} \color{blue}{-30} \\\Leftrightarrow & 525x+70x& = & 14-30 \\\Leftrightarrow & \color{red}{595} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{595} & & \\ & V = \left\{ \frac{-16}{595} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+90} & = & \color{red}{-105x} +28 \\\Leftrightarrow & -252x \color{red}{+90} \color{blue}{-90} \color{blue}{+105x} & = & \color{red}{-105x} +28 \color{blue}{+105x} \color{blue}{-90} \\\Leftrightarrow & -252x+105x& = & 28-90 \\\Leftrightarrow & \color{red}{-147} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-147} & & \\\Leftrightarrow & x = \frac{62}{147} & & \\ & V = \left\{ \frac{62}{147} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{11})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 20x-\frac{12}{11}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-84} & = & \color{red}{-231x} +33 \\\Leftrightarrow & 1540x \color{red}{-84} \color{blue}{+84} \color{blue}{+231x} & = & \color{red}{-231x} +33 \color{blue}{+231x} \color{blue}{+84} \\\Leftrightarrow & 1540x+231x& = & 33+84 \\\Leftrightarrow & \color{red}{1771} x& = & 117 \\\Leftrightarrow & x = \frac{117}{1771} & & \\ & V = \left\{ \frac{117}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{7})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-36} & = & \color{red}{105x} +56 \\\Leftrightarrow & -252x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +56 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -252x-105x& = & 56+36 \\\Leftrightarrow & \color{red}{-357} x& = & 92 \\\Leftrightarrow & x = \frac{92}{-357} & & \\\Leftrightarrow & x = \frac{-92}{357} & & \\ & V = \left\{ \frac{-92}{357} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 6x-\frac{15}{4}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{60x} +40 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & 72x-60x& = & 40+45 \\\Leftrightarrow & \color{red}{12} x& = & 85 \\\Leftrightarrow & x = \frac{85}{12} & & \\ & V = \left\{ \frac{85}{12} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{5})& = & -3x+\frac{3}{11} \\\Leftrightarrow & -14x+\frac{14}{5}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x+ \frac{154}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{+154} & = & \color{red}{-165x} +15 \\\Leftrightarrow & -770x \color{red}{+154} \color{blue}{-154} \color{blue}{+165x} & = & \color{red}{-165x} +15 \color{blue}{+165x} \color{blue}{-154} \\\Leftrightarrow & -770x+165x& = & 15-154 \\\Leftrightarrow & \color{red}{-605} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-605} & & \\\Leftrightarrow & x = \frac{139}{605} & & \\ & V = \left\{ \frac{139}{605} \right\} & \\\end{align}\)
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