Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{8}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+88} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -924x \color{red}{+88} \color{blue}{-88} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-88} \\\Leftrightarrow & -924x+385x& = & 42-88 \\\Leftrightarrow & \color{red}{-539} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{-539} & & \\\Leftrightarrow & x = \frac{46}{539} & & \\ & V = \left\{ \frac{46}{539} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{2}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -14x+\frac{14}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -490x \color{red}{+98} & = & \color{red}{175x} +50 \\\Leftrightarrow & -490x \color{red}{+98} \color{blue}{-98} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-98} \\\Leftrightarrow & -490x-175x& = & 50-98 \\\Leftrightarrow & \color{red}{-665} x& = & -48 \\\Leftrightarrow & x = \frac{-48}{-665} & & \\\Leftrightarrow & x = \frac{48}{665} & & \\ & V = \left\{ \frac{48}{665} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 15x+\frac{9}{10}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1350}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} })& = & (\frac{630}{ \color{blue}{90} }x+ \frac{20}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1350x \color{red}{+81} & = & \color{red}{630x} +20 \\\Leftrightarrow & 1350x \color{red}{+81} \color{blue}{-81} \color{blue}{-630x} & = & \color{red}{630x} +20 \color{blue}{-630x} \color{blue}{-81} \\\Leftrightarrow & 1350x-630x& = & 20-81 \\\Leftrightarrow & \color{red}{720} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{720} & & \\ & V = \left\{ \frac{-61}{720} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +49 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +49 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 49+110 \\\Leftrightarrow & \color{red}{-231} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-231} & & \\\Leftrightarrow & x = \frac{-53}{77} & & \\ & V = \left\{ \frac{-53}{77} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{11})& = & -4x+\frac{9}{8} \\\Leftrightarrow & -15x+\frac{15}{11}& = & -4x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1320}{ \color{blue}{88} }x+ \frac{120}{ \color{blue}{88} })& = & (\frac{-352}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1320x \color{red}{+120} & = & \color{red}{-352x} +99 \\\Leftrightarrow & -1320x \color{red}{+120} \color{blue}{-120} \color{blue}{+352x} & = & \color{red}{-352x} +99 \color{blue}{+352x} \color{blue}{-120} \\\Leftrightarrow & -1320x+352x& = & 99-120 \\\Leftrightarrow & \color{red}{-968} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-968} & & \\\Leftrightarrow & x = \frac{21}{968} & & \\ & V = \left\{ \frac{21}{968} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+132} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 660x \color{red}{+132} \color{blue}{-132} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{-132} \\\Leftrightarrow & 660x+275x& = & 25-132 \\\Leftrightarrow & \color{red}{935} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{935} & & \\ & V = \left\{ \frac{-107}{935} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 360x \color{red}{+40} & = & \color{red}{135x} +54 \\\Leftrightarrow & 360x \color{red}{+40} \color{blue}{-40} \color{blue}{-135x} & = & \color{red}{135x} +54 \color{blue}{-135x} \color{blue}{-40} \\\Leftrightarrow & 360x-135x& = & 54-40 \\\Leftrightarrow & \color{red}{225} x& = & 14 \\\Leftrightarrow & x = \frac{14}{225} & & \\ & V = \left\{ \frac{14}{225} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{12})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{25}{12}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1200}{ \color{blue}{60} }x- \frac{125}{ \color{blue}{60} })& = & (\frac{-180}{ \color{blue}{60} }x+ \frac{48}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1200x \color{red}{-125} & = & \color{red}{-180x} +48 \\\Leftrightarrow & 1200x \color{red}{-125} \color{blue}{+125} \color{blue}{+180x} & = & \color{red}{-180x} +48 \color{blue}{+180x} \color{blue}{+125} \\\Leftrightarrow & 1200x+180x& = & 48+125 \\\Leftrightarrow & \color{red}{1380} x& = & 173 \\\Leftrightarrow & x = \frac{173}{1380} & & \\ & V = \left\{ \frac{173}{1380} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{9})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{+32} & = & \color{red}{252x} +21 \\\Leftrightarrow & -360x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -360x-252x& = & 21-32 \\\Leftrightarrow & \color{red}{-612} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-612} & & \\\Leftrightarrow & x = \frac{11}{612} & & \\ & V = \left\{ \frac{11}{612} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-75} & = & \color{red}{180x} +32 \\\Leftrightarrow & -400x \color{red}{-75} \color{blue}{+75} \color{blue}{-180x} & = & \color{red}{180x} +32 \color{blue}{-180x} \color{blue}{+75} \\\Leftrightarrow & -400x-180x& = & 32+75 \\\Leftrightarrow & \color{red}{-580} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-580} & & \\\Leftrightarrow & x = \frac{-107}{580} & & \\ & V = \left\{ \frac{-107}{580} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{2})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 12x+\frac{9}{2}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{216}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{10}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 216x \color{red}{+81} & = & \color{red}{90x} +10 \\\Leftrightarrow & 216x \color{red}{+81} \color{blue}{-81} \color{blue}{-90x} & = & \color{red}{90x} +10 \color{blue}{-90x} \color{blue}{-81} \\\Leftrightarrow & 216x-90x& = & 10-81 \\\Leftrightarrow & \color{red}{126} x& = & -71 \\\Leftrightarrow & x = \frac{-71}{126} & & \\ & V = \left\{ \frac{-71}{126} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{4}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+4} & = & \color{red}{-27x} +4 \\\Leftrightarrow & 24x \color{red}{+4} \color{blue}{-4} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{-4} \\\Leftrightarrow & 24x+27x& = & 4-4 \\\Leftrightarrow & \color{red}{51} x& = & 0 \\\Leftrightarrow & x = \frac{0}{51} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
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