Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{11})& = & -8x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{15}{11}& = & -8x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x+ \frac{30}{ \color{blue}{22} })& = & (\frac{-176}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{+30} & = & \color{red}{-176x} +99 \\\Leftrightarrow & -330x \color{red}{+30} \color{blue}{-30} \color{blue}{+176x} & = & \color{red}{-176x} +99 \color{blue}{+176x} \color{blue}{-30} \\\Leftrightarrow & -330x+176x& = & 99-30 \\\Leftrightarrow & \color{red}{-154} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-154} & & \\\Leftrightarrow & x = \frac{-69}{154} & & \\ & V = \left\{ \frac{-69}{154} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{3})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+20} & = & \color{red}{-21x} +4 \\\Leftrightarrow & -48x \color{red}{+20} \color{blue}{-20} \color{blue}{+21x} & = & \color{red}{-21x} +4 \color{blue}{+21x} \color{blue}{-20} \\\Leftrightarrow & -48x+21x& = & 4-20 \\\Leftrightarrow & \color{red}{-27} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-27} & & \\\Leftrightarrow & x = \frac{16}{27} & & \\ & V = \left\{ \frac{16}{27} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{6}{11}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-528}{ \color{blue}{66} }x- \frac{36}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{594x} +55 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{-594x} & = & \color{red}{594x} +55 \color{blue}{-594x} \color{blue}{+36} \\\Leftrightarrow & -528x-594x& = & 55+36 \\\Leftrightarrow & \color{red}{-1122} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-1122} & & \\\Leftrightarrow & x = \frac{-91}{1122} & & \\ & V = \left\{ \frac{-91}{1122} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{6}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{45x} +20 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{+18} \\\Leftrightarrow & 150x-45x& = & 20+18 \\\Leftrightarrow & \color{red}{105} x& = & 38 \\\Leftrightarrow & x = \frac{38}{105} & & \\ & V = \left\{ \frac{38}{105} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{176}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+176} & = & \color{red}{-165x} +6 \\\Leftrightarrow & -396x \color{red}{+176} \color{blue}{-176} \color{blue}{+165x} & = & \color{red}{-165x} +6 \color{blue}{+165x} \color{blue}{-176} \\\Leftrightarrow & -396x+165x& = & 6-176 \\\Leftrightarrow & \color{red}{-231} x& = & -170 \\\Leftrightarrow & x = \frac{-170}{-231} & & \\\Leftrightarrow & x = \frac{170}{231} & & \\ & V = \left\{ \frac{170}{231} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{6})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 25x-\frac{25}{6}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{-25} & = & \color{red}{12x} +4 \\\Leftrightarrow & 150x \color{red}{-25} \color{blue}{+25} \color{blue}{-12x} & = & \color{red}{12x} +4 \color{blue}{-12x} \color{blue}{+25} \\\Leftrightarrow & 150x-12x& = & 4+25 \\\Leftrightarrow & \color{red}{138} x& = & 29 \\\Leftrightarrow & x = \frac{29}{138} & & \\ & V = \left\{ \frac{29}{138} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+12} & = & \color{red}{98x} +21 \\\Leftrightarrow & -140x \color{red}{+12} \color{blue}{-12} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{-12} \\\Leftrightarrow & -140x-98x& = & 21-12 \\\Leftrightarrow & \color{red}{-238} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-238} & & \\\Leftrightarrow & x = \frac{-9}{238} & & \\ & V = \left\{ \frac{-9}{238} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{9})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 14x-\frac{14}{9}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{882}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 882x \color{red}{-98} & = & \color{red}{-567x} +90 \\\Leftrightarrow & 882x \color{red}{-98} \color{blue}{+98} \color{blue}{+567x} & = & \color{red}{-567x} +90 \color{blue}{+567x} \color{blue}{+98} \\\Leftrightarrow & 882x+567x& = & 90+98 \\\Leftrightarrow & \color{red}{1449} x& = & 188 \\\Leftrightarrow & x = \frac{188}{1449} & & \\ & V = \left\{ \frac{188}{1449} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 14+50 \\\Leftrightarrow & \color{red}{-105} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-105} & & \\\Leftrightarrow & x = \frac{-64}{105} & & \\ & V = \left\{ \frac{-64}{105} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 15x+\frac{9}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+99} & = & \color{red}{385x} +10 \\\Leftrightarrow & 825x \color{red}{+99} \color{blue}{-99} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{-99} \\\Leftrightarrow & 825x-385x& = & 10-99 \\\Leftrightarrow & \color{red}{440} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{440} & & \\ & V = \left\{ \frac{-89}{440} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{9})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -35x-\frac{14}{9}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x- \frac{28}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{-28} & = & \color{red}{-162x} +27 \\\Leftrightarrow & -630x \color{red}{-28} \color{blue}{+28} \color{blue}{+162x} & = & \color{red}{-162x} +27 \color{blue}{+162x} \color{blue}{+28} \\\Leftrightarrow & -630x+162x& = & 27+28 \\\Leftrightarrow & \color{red}{-468} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-468} & & \\\Leftrightarrow & x = \frac{-55}{468} & & \\ & V = \left\{ \frac{-55}{468} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{5}{11})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 4x+\frac{10}{11}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{+90} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 396x \color{red}{+90} \color{blue}{-90} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{-90} \\\Leftrightarrow & 396x+297x& = & 22-90 \\\Leftrightarrow & \color{red}{693} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{693} & & \\ & V = \left\{ \frac{-68}{693} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-06-25 09:52:22
Een site van Busleyden Atheneum Mechelen