Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{7})& = & 3x+\frac{5}{9} \\\Leftrightarrow & 10x-\frac{20}{7}& = & 3x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{180}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-180} & = & \color{red}{189x} +35 \\\Leftrightarrow & 630x \color{red}{-180} \color{blue}{+180} \color{blue}{-189x} & = & \color{red}{189x} +35 \color{blue}{-189x} \color{blue}{+180} \\\Leftrightarrow & 630x-189x& = & 35+180 \\\Leftrightarrow & \color{red}{441} x& = & 215 \\\Leftrightarrow & x = \frac{215}{441} & & \\ & V = \left\{ \frac{215}{441} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{10}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{+50} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 440x \color{red}{+50} \color{blue}{-50} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{-50} \\\Leftrightarrow & 440x+385x& = & 66-50 \\\Leftrightarrow & \color{red}{825} x& = & 16 \\\Leftrightarrow & x = \frac{16}{825} & & \\ & V = \left\{ \frac{16}{825} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{3})& = & -2x+\frac{6}{11} \\\Leftrightarrow & 35x+\frac{28}{3}& = & -2x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+308} & = & \color{red}{-66x} +18 \\\Leftrightarrow & 1155x \color{red}{+308} \color{blue}{-308} \color{blue}{+66x} & = & \color{red}{-66x} +18 \color{blue}{+66x} \color{blue}{-308} \\\Leftrightarrow & 1155x+66x& = & 18-308 \\\Leftrightarrow & \color{red}{1221} x& = & -290 \\\Leftrightarrow & x = \frac{-290}{1221} & & \\ & V = \left\{ \frac{-290}{1221} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{11})& = & 7x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{20}{11}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x- \frac{100}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{-100} & = & \color{red}{385x} +44 \\\Leftrightarrow & -1100x \color{red}{-100} \color{blue}{+100} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{+100} \\\Leftrightarrow & -1100x-385x& = & 44+100 \\\Leftrightarrow & \color{red}{-1485} x& = & 144 \\\Leftrightarrow & x = \frac{144}{-1485} & & \\\Leftrightarrow & x = \frac{-16}{165} & & \\ & V = \left\{ \frac{-16}{165} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{4}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 24x+\frac{24}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x+ \frac{120}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{-120} \\\Leftrightarrow & 840x+175x& = & 42-120 \\\Leftrightarrow & \color{red}{1015} x& = & -78 \\\Leftrightarrow & x = \frac{-78}{1015} & & \\ & V = \left\{ \frac{-78}{1015} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 8x+\frac{5}{2} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{+28} & = & \color{red}{48x} +15 \\\Leftrightarrow & 126x \color{red}{+28} \color{blue}{-28} \color{blue}{-48x} & = & \color{red}{48x} +15 \color{blue}{-48x} \color{blue}{-28} \\\Leftrightarrow & 126x-48x& = & 15-28 \\\Leftrightarrow & \color{red}{78} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{78} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 660x+275x& = & 50+132 \\\Leftrightarrow & \color{red}{935} x& = & 182 \\\Leftrightarrow & x = \frac{182}{935} & & \\ & V = \left\{ \frac{182}{935} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{5}{7})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{25}{7}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{125}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-125} & = & \color{red}{-280x} +42 \\\Leftrightarrow & -525x \color{red}{-125} \color{blue}{+125} \color{blue}{+280x} & = & \color{red}{-280x} +42 \color{blue}{+280x} \color{blue}{+125} \\\Leftrightarrow & -525x+280x& = & 42+125 \\\Leftrightarrow & \color{red}{-245} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-245} & & \\\Leftrightarrow & x = \frac{-167}{245} & & \\ & V = \left\{ \frac{-167}{245} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{8})& = & 2x+\frac{8}{11} \\\Leftrightarrow & -25x-\frac{15}{8}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{-165} & = & \color{red}{176x} +64 \\\Leftrightarrow & -2200x \color{red}{-165} \color{blue}{+165} \color{blue}{-176x} & = & \color{red}{176x} +64 \color{blue}{-176x} \color{blue}{+165} \\\Leftrightarrow & -2200x-176x& = & 64+165 \\\Leftrightarrow & \color{red}{-2376} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-2376} & & \\\Leftrightarrow & x = \frac{-229}{2376} & & \\ & V = \left\{ \frac{-229}{2376} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x-\frac{12}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{36}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-36} & = & \color{red}{147x} +28 \\\Leftrightarrow & -126x \color{red}{-36} \color{blue}{+36} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+36} \\\Leftrightarrow & -126x-147x& = & 28+36 \\\Leftrightarrow & \color{red}{-273} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-273} & & \\\Leftrightarrow & x = \frac{-64}{273} & & \\ & V = \left\{ \frac{-64}{273} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{7})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{12}{7}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{108}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-108} & = & \color{red}{315x} +70 \\\Leftrightarrow & -756x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +70 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -756x-315x& = & 70+108 \\\Leftrightarrow & \color{red}{-1071} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-1071} & & \\\Leftrightarrow & x = \frac{-178}{1071} & & \\ & V = \left\{ \frac{-178}{1071} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{3})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -25x+\frac{20}{3}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-600}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -600x \color{red}{+160} & = & \color{red}{-120x} +27 \\\Leftrightarrow & -600x \color{red}{+160} \color{blue}{-160} \color{blue}{+120x} & = & \color{red}{-120x} +27 \color{blue}{+120x} \color{blue}{-160} \\\Leftrightarrow & -600x+120x& = & 27-160 \\\Leftrightarrow & \color{red}{-480} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{-480} & & \\\Leftrightarrow & x = \frac{133}{480} & & \\ & V = \left\{ \frac{133}{480} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-02-08 21:14:55
Een site van Busleyden Atheneum Mechelen