Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{25}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{125}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+125} & = & \color{red}{385x} +66 \\\Leftrightarrow & 550x \color{red}{+125} \color{blue}{-125} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-125} \\\Leftrightarrow & 550x-385x& = & 66-125 \\\Leftrightarrow & \color{red}{165} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{165} & & \\ & V = \left\{ \frac{-59}{165} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & 7x+\frac{2}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{245x} +10 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +10 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & 420x-245x& = & 10+84 \\\Leftrightarrow & \color{red}{175} x& = & 94 \\\Leftrightarrow & x = \frac{94}{175} & & \\ & V = \left\{ \frac{94}{175} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{3})& = & -5x+\frac{7}{12} \\\Leftrightarrow & -12x-\frac{16}{3}& = & -5x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{64}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-64} & = & \color{red}{-60x} +7 \\\Leftrightarrow & -144x \color{red}{-64} \color{blue}{+64} \color{blue}{+60x} & = & \color{red}{-60x} +7 \color{blue}{+60x} \color{blue}{+64} \\\Leftrightarrow & -144x+60x& = & 7+64 \\\Leftrightarrow & \color{red}{-84} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-84} & & \\\Leftrightarrow & x = \frac{-71}{84} & & \\ & V = \left\{ \frac{-71}{84} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -35x-\frac{35}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-105}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -105x \color{red}{-35} & = & \color{red}{-27x} +4 \\\Leftrightarrow & -105x \color{red}{-35} \color{blue}{+35} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+35} \\\Leftrightarrow & -105x+27x& = & 4+35 \\\Leftrightarrow & \color{red}{-78} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-78} & & \\\Leftrightarrow & x = \frac{-1}{2} & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x-\frac{16}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{-16} & = & \color{red}{9x} +4 \\\Leftrightarrow & 48x \color{red}{-16} \color{blue}{+16} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{+16} \\\Leftrightarrow & 48x-9x& = & 4+16 \\\Leftrightarrow & \color{red}{39} x& = & 20 \\\Leftrightarrow & x = \frac{20}{39} & & \\ & V = \left\{ \frac{20}{39} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & 7x+\frac{3}{5} \\\Leftrightarrow & -25x-\frac{15}{4}& = & 7x+\frac{3}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{12}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-75} & = & \color{red}{140x} +12 \\\Leftrightarrow & -500x \color{red}{-75} \color{blue}{+75} \color{blue}{-140x} & = & \color{red}{140x} +12 \color{blue}{-140x} \color{blue}{+75} \\\Leftrightarrow & -500x-140x& = & 12+75 \\\Leftrightarrow & \color{red}{-640} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-640} & & \\\Leftrightarrow & x = \frac{-87}{640} & & \\ & V = \left\{ \frac{-87}{640} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{6})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -14x-\frac{35}{6}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-588}{ \color{blue}{42} }x- \frac{245}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -588x \color{red}{-245} & = & \color{red}{210x} +60 \\\Leftrightarrow & -588x \color{red}{-245} \color{blue}{+245} \color{blue}{-210x} & = & \color{red}{210x} +60 \color{blue}{-210x} \color{blue}{+245} \\\Leftrightarrow & -588x-210x& = & 60+245 \\\Leftrightarrow & \color{red}{-798} x& = & 305 \\\Leftrightarrow & x = \frac{305}{-798} & & \\\Leftrightarrow & x = \frac{-305}{798} & & \\ & V = \left\{ \frac{-305}{798} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{4}{5})& = & 2x+\frac{3}{4} \\\Leftrightarrow & -18x+\frac{24}{5}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-360}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -360x \color{red}{+96} & = & \color{red}{40x} +15 \\\Leftrightarrow & -360x \color{red}{+96} \color{blue}{-96} \color{blue}{-40x} & = & \color{red}{40x} +15 \color{blue}{-40x} \color{blue}{-96} \\\Leftrightarrow & -360x-40x& = & 15-96 \\\Leftrightarrow & \color{red}{-400} x& = & -81 \\\Leftrightarrow & x = \frac{-81}{-400} & & \\\Leftrightarrow & x = \frac{81}{400} & & \\ & V = \left\{ \frac{81}{400} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{11})& = & 9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{8}{11}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{+8} & = & \color{red}{99x} +5 \\\Leftrightarrow & -88x \color{red}{+8} \color{blue}{-8} \color{blue}{-99x} & = & \color{red}{99x} +5 \color{blue}{-99x} \color{blue}{-8} \\\Leftrightarrow & -88x-99x& = & 5-8 \\\Leftrightarrow & \color{red}{-187} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-187} & & \\\Leftrightarrow & x = \frac{3}{187} & & \\ & V = \left\{ \frac{3}{187} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{3})& = & 7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{10}{3}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+50} & = & \color{red}{105x} +6 \\\Leftrightarrow & -90x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & -90x-105x& = & 6-50 \\\Leftrightarrow & \color{red}{-195} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-195} & & \\\Leftrightarrow & x = \frac{44}{195} & & \\ & V = \left\{ \frac{44}{195} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{+330} & = & \color{red}{385x} +42 \\\Leftrightarrow & 1848x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & 1848x-385x& = & 42-330 \\\Leftrightarrow & \color{red}{1463} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{1463} & & \\ & V = \left\{ \frac{-288}{1463} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x- \frac{144}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{-144} & = & \color{red}{441x} +28 \\\Leftrightarrow & -1008x \color{red}{-144} \color{blue}{+144} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{+144} \\\Leftrightarrow & -1008x-441x& = & 28+144 \\\Leftrightarrow & \color{red}{-1449} x& = & 172 \\\Leftrightarrow & x = \frac{172}{-1449} & & \\\Leftrightarrow & x = \frac{-172}{1449} & & \\ & V = \left\{ \frac{-172}{1449} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-11 02:45:56
Een site van Busleyden Atheneum Mechelen