Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{+135} & = & \color{red}{108x} +32 \\\Leftrightarrow & -720x \color{red}{+135} \color{blue}{-135} \color{blue}{-108x} & = & \color{red}{108x} +32 \color{blue}{-108x} \color{blue}{-135} \\\Leftrightarrow & -720x-108x& = & 32-135 \\\Leftrightarrow & \color{red}{-828} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-828} & & \\\Leftrightarrow & x = \frac{103}{828} & & \\ & V = \left\{ \frac{103}{828} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{24}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{420}{ \color{blue}{14} }x- \frac{48}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 420x \color{red}{-48} & = & \color{red}{98x} +21 \\\Leftrightarrow & 420x \color{red}{-48} \color{blue}{+48} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+48} \\\Leftrightarrow & 420x-98x& = & 21+48 \\\Leftrightarrow & \color{red}{322} x& = & 69 \\\Leftrightarrow & x = \frac{69}{322} & & \\\Leftrightarrow & x = \frac{3}{14} & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{3})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -10x-\frac{8}{3}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{147x} +12 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{-147x} & = & \color{red}{147x} +12 \color{blue}{-147x} \color{blue}{+56} \\\Leftrightarrow & -210x-147x& = & 12+56 \\\Leftrightarrow & \color{red}{-357} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-357} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{2}{5})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +15 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +15 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 15+84 \\\Leftrightarrow & \color{red}{-595} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-595} & & \\\Leftrightarrow & x = \frac{-99}{595} & & \\ & V = \left\{ \frac{-99}{595} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{3})& = & 9x+\frac{3}{10} \\\Leftrightarrow & 25x-\frac{25}{3}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{750}{ \color{blue}{30} }x- \frac{250}{ \color{blue}{30} })& = & (\frac{270}{ \color{blue}{30} }x+ \frac{9}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 750x \color{red}{-250} & = & \color{red}{270x} +9 \\\Leftrightarrow & 750x \color{red}{-250} \color{blue}{+250} \color{blue}{-270x} & = & \color{red}{270x} +9 \color{blue}{-270x} \color{blue}{+250} \\\Leftrightarrow & 750x-270x& = & 9+250 \\\Leftrightarrow & \color{red}{480} x& = & 259 \\\Leftrightarrow & x = \frac{259}{480} & & \\ & V = \left\{ \frac{259}{480} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{11})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -21x-\frac{28}{11}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-462}{ \color{blue}{22} }x- \frac{56}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -462x \color{red}{-56} & = & \color{red}{-176x} +33 \\\Leftrightarrow & -462x \color{red}{-56} \color{blue}{+56} \color{blue}{+176x} & = & \color{red}{-176x} +33 \color{blue}{+176x} \color{blue}{+56} \\\Leftrightarrow & -462x+176x& = & 33+56 \\\Leftrightarrow & \color{red}{-286} x& = & 89 \\\Leftrightarrow & x = \frac{89}{-286} & & \\\Leftrightarrow & x = \frac{-89}{286} & & \\ & V = \left\{ \frac{-89}{286} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{15}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{135}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+135} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1188x \color{red}{+135} \color{blue}{-135} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{-135} \\\Leftrightarrow & -1188x-495x& = & 88-135 \\\Leftrightarrow & \color{red}{-1683} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-1683} & & \\\Leftrightarrow & x = \frac{47}{1683} & & \\ & V = \left\{ \frac{47}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{7})& = & 9x+\frac{7}{11} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 9x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+220} & = & \color{red}{693x} +49 \\\Leftrightarrow & -1925x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +49 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & -1925x-693x& = & 49-220 \\\Leftrightarrow & \color{red}{-2618} x& = & -171 \\\Leftrightarrow & x = \frac{-171}{-2618} & & \\\Leftrightarrow & x = \frac{171}{2618} & & \\ & V = \left\{ \frac{171}{2618} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & -8x+\frac{9}{11} \\\Leftrightarrow & -15x+\frac{20}{3}& = & -8x+\frac{9}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{27}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+220} & = & \color{red}{-264x} +27 \\\Leftrightarrow & -495x \color{red}{+220} \color{blue}{-220} \color{blue}{+264x} & = & \color{red}{-264x} +27 \color{blue}{+264x} \color{blue}{-220} \\\Leftrightarrow & -495x+264x& = & 27-220 \\\Leftrightarrow & \color{red}{-231} x& = & -193 \\\Leftrightarrow & x = \frac{-193}{-231} & & \\\Leftrightarrow & x = \frac{193}{231} & & \\ & V = \left\{ \frac{193}{231} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{3})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 16x+\frac{20}{3}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+20} & = & \color{red}{-27x} +8 \\\Leftrightarrow & 48x \color{red}{+20} \color{blue}{-20} \color{blue}{+27x} & = & \color{red}{-27x} +8 \color{blue}{+27x} \color{blue}{-20} \\\Leftrightarrow & 48x+27x& = & 8-20 \\\Leftrightarrow & \color{red}{75} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{75} & & \\\Leftrightarrow & x = \frac{-4}{25} & & \\ & V = \left\{ \frac{-4}{25} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{16}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+112} & = & \color{red}{385x} +22 \\\Leftrightarrow & -924x \color{red}{+112} \color{blue}{-112} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-112} \\\Leftrightarrow & -924x-385x& = & 22-112 \\\Leftrightarrow & \color{red}{-1309} x& = & -90 \\\Leftrightarrow & x = \frac{-90}{-1309} & & \\\Leftrightarrow & x = \frac{90}{1309} & & \\ & V = \left\{ \frac{90}{1309} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{10})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{9}{10}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-99} & = & \color{red}{550x} +100 \\\Leftrightarrow & -1320x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +100 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & -1320x-550x& = & 100+99 \\\Leftrightarrow & \color{red}{-1870} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-1870} & & \\\Leftrightarrow & x = \frac{-199}{1870} & & \\ & V = \left\{ \frac{-199}{1870} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-11-12 00:44:34
Een site van Busleyden Atheneum Mechelen