Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & 8x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & 8x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{192x} +64 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{-192x} & = & \color{red}{192x} +64 \color{blue}{-192x} \color{blue}{-63} \\\Leftrightarrow & 504x-192x& = & 64-63 \\\Leftrightarrow & \color{red}{312} x& = & 1 \\\Leftrightarrow & x = \frac{1}{312} & & \\ & V = \left\{ \frac{1}{312} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{2}{7})& = & -3x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{8}{7}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{40}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-40} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -280x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & -280x+105x& = & 56+40 \\\Leftrightarrow & \color{red}{-175} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-175} & & \\\Leftrightarrow & x = \frac{-96}{175} & & \\ & V = \left\{ \frac{-96}{175} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x+ \frac{250}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{+250} & = & \color{red}{490x} +21 \\\Leftrightarrow & -700x \color{red}{+250} \color{blue}{-250} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{-250} \\\Leftrightarrow & -700x-490x& = & 21-250 \\\Leftrightarrow & \color{red}{-1190} x& = & -229 \\\Leftrightarrow & x = \frac{-229}{-1190} & & \\\Leftrightarrow & x = \frac{229}{1190} & & \\ & V = \left\{ \frac{229}{1190} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{3}{7})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{18}{7}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-504}{ \color{blue}{42} }x+ \frac{108}{ \color{blue}{42} })& = & (\frac{-210}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -504x \color{red}{+108} & = & \color{red}{-210x} +35 \\\Leftrightarrow & -504x \color{red}{+108} \color{blue}{-108} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-108} \\\Leftrightarrow & -504x+210x& = & 35-108 \\\Leftrightarrow & \color{red}{-294} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-294} & & \\\Leftrightarrow & x = \frac{73}{294} & & \\ & V = \left\{ \frac{73}{294} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{105x} +40 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 180x-105x& = & 40+36 \\\Leftrightarrow & \color{red}{75} x& = & 76 \\\Leftrightarrow & x = \frac{76}{75} & & \\ & V = \left\{ \frac{76}{75} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{11})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 14x-\frac{28}{11}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-196} & = & \color{red}{231x} +110 \\\Leftrightarrow & 1078x \color{red}{-196} \color{blue}{+196} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+196} \\\Leftrightarrow & 1078x-231x& = & 110+196 \\\Leftrightarrow & \color{red}{847} x& = & 306 \\\Leftrightarrow & x = \frac{306}{847} & & \\ & V = \left\{ \frac{306}{847} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{6})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{6}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{300}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{-90}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 300x \color{red}{+125} & = & \color{red}{-90x} +36 \\\Leftrightarrow & 300x \color{red}{+125} \color{blue}{-125} \color{blue}{+90x} & = & \color{red}{-90x} +36 \color{blue}{+90x} \color{blue}{-125} \\\Leftrightarrow & 300x+90x& = & 36-125 \\\Leftrightarrow & \color{red}{390} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{390} & & \\ & V = \left\{ \frac{-89}{390} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{3}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{12}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+60} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 280x \color{red}{+60} \color{blue}{-60} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-60} \\\Leftrightarrow & 280x+245x& = & 42-60 \\\Leftrightarrow & \color{red}{525} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{525} & & \\\Leftrightarrow & x = \frac{-6}{175} & & \\ & V = \left\{ \frac{-6}{175} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{9})& = & -3x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{10}{9}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-144}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{-54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -144x \color{red}{+20} & = & \color{red}{-54x} +81 \\\Leftrightarrow & -144x \color{red}{+20} \color{blue}{-20} \color{blue}{+54x} & = & \color{red}{-54x} +81 \color{blue}{+54x} \color{blue}{-20} \\\Leftrightarrow & -144x+54x& = & 81-20 \\\Leftrightarrow & \color{red}{-90} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-90} & & \\\Leftrightarrow & x = \frac{-61}{90} & & \\ & V = \left\{ \frac{-61}{90} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{11})& = & -5x+\frac{3}{4} \\\Leftrightarrow & -12x-\frac{20}{11}& = & -5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x- \frac{80}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{-80} & = & \color{red}{-220x} +33 \\\Leftrightarrow & -528x \color{red}{-80} \color{blue}{+80} \color{blue}{+220x} & = & \color{red}{-220x} +33 \color{blue}{+220x} \color{blue}{+80} \\\Leftrightarrow & -528x+220x& = & 33+80 \\\Leftrightarrow & \color{red}{-308} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-308} & & \\\Leftrightarrow & x = \frac{-113}{308} & & \\ & V = \left\{ \frac{-113}{308} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{10}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+50} & = & \color{red}{-245x} +42 \\\Leftrightarrow & -350x \color{red}{+50} \color{blue}{-50} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{-50} \\\Leftrightarrow & -350x+245x& = & 42-50 \\\Leftrightarrow & \color{red}{-105} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-105} & & \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{105x} +24 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & 120x-105x& = & 24-40 \\\Leftrightarrow & \color{red}{15} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{15} & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-02 19:38:42
Een site van Busleyden Atheneum Mechelen