Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -16x+\frac{20}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{60}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+60} & = & \color{red}{231x} +110 \\\Leftrightarrow & -528x \color{red}{+60} \color{blue}{-60} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{-60} \\\Leftrightarrow & -528x-231x& = & 110-60 \\\Leftrightarrow & \color{red}{-759} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-759} & & \\\Leftrightarrow & x = \frac{-50}{759} & & \\ & V = \left\{ \frac{-50}{759} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 4x-\frac{10}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{440}{ \color{blue}{110} }x- \frac{100}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 440x \color{red}{-100} & = & \color{red}{-330x} +99 \\\Leftrightarrow & 440x \color{red}{-100} \color{blue}{+100} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{+100} \\\Leftrightarrow & 440x+330x& = & 99+100 \\\Leftrightarrow & \color{red}{770} x& = & 199 \\\Leftrightarrow & x = \frac{199}{770} & & \\ & V = \left\{ \frac{199}{770} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{7})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{-49x} +4 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{+49x} & = & \color{red}{-49x} +4 \color{blue}{+49x} \color{blue}{+20} \\\Leftrightarrow & -112x+49x& = & 4+20 \\\Leftrightarrow & \color{red}{-63} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-63} & & \\\Leftrightarrow & x = \frac{-8}{21} & & \\ & V = \left\{ \frac{-8}{21} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{9})& = & 9x+\frac{8}{7} \\\Leftrightarrow & -35x+\frac{28}{9}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-2205}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -2205x \color{red}{+196} & = & \color{red}{567x} +72 \\\Leftrightarrow & -2205x \color{red}{+196} \color{blue}{-196} \color{blue}{-567x} & = & \color{red}{567x} +72 \color{blue}{-567x} \color{blue}{-196} \\\Leftrightarrow & -2205x-567x& = & 72-196 \\\Leftrightarrow & \color{red}{-2772} x& = & -124 \\\Leftrightarrow & x = \frac{-124}{-2772} & & \\\Leftrightarrow & x = \frac{31}{693} & & \\ & V = \left\{ \frac{31}{693} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & -4x+\frac{3}{7} \\\Leftrightarrow & -15x-\frac{20}{9}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-140} & = & \color{red}{-252x} +27 \\\Leftrightarrow & -945x \color{red}{-140} \color{blue}{+140} \color{blue}{+252x} & = & \color{red}{-252x} +27 \color{blue}{+252x} \color{blue}{+140} \\\Leftrightarrow & -945x+252x& = & 27+140 \\\Leftrightarrow & \color{red}{-693} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-693} & & \\\Leftrightarrow & x = \frac{-167}{693} & & \\ & V = \left\{ \frac{-167}{693} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{5}{11})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -24x+\frac{30}{11}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x+ \frac{120}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{+120} & = & \color{red}{-220x} +77 \\\Leftrightarrow & -1056x \color{red}{+120} \color{blue}{-120} \color{blue}{+220x} & = & \color{red}{-220x} +77 \color{blue}{+220x} \color{blue}{-120} \\\Leftrightarrow & -1056x+220x& = & 77-120 \\\Leftrightarrow & \color{red}{-836} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-836} & & \\\Leftrightarrow & x = \frac{43}{836} & & \\ & V = \left\{ \frac{43}{836} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+36} & = & \color{red}{-60x} +20 \\\Leftrightarrow & 225x \color{red}{+36} \color{blue}{-36} \color{blue}{+60x} & = & \color{red}{-60x} +20 \color{blue}{+60x} \color{blue}{-36} \\\Leftrightarrow & 225x+60x& = & 20-36 \\\Leftrightarrow & \color{red}{285} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{285} & & \\ & V = \left\{ \frac{-16}{285} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+24} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 252x \color{red}{+24} \color{blue}{-24} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-24} \\\Leftrightarrow & 252x+105x& = & 70-24 \\\Leftrightarrow & \color{red}{357} x& = & 46 \\\Leftrightarrow & x = \frac{46}{357} & & \\ & V = \left\{ \frac{46}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{2}{11})& = & 4x+\frac{7}{8} \\\Leftrightarrow & 15x+\frac{10}{11}& = & 4x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{352}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+80} & = & \color{red}{352x} +77 \\\Leftrightarrow & 1320x \color{red}{+80} \color{blue}{-80} \color{blue}{-352x} & = & \color{red}{352x} +77 \color{blue}{-352x} \color{blue}{-80} \\\Leftrightarrow & 1320x-352x& = & 77-80 \\\Leftrightarrow & \color{red}{968} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{968} & & \\ & V = \left\{ \frac{-3}{968} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{15}{2}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-45} & = & \color{red}{-30x} +4 \\\Leftrightarrow & 72x \color{red}{-45} \color{blue}{+45} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{+45} \\\Leftrightarrow & 72x+30x& = & 4+45 \\\Leftrightarrow & \color{red}{102} x& = & 49 \\\Leftrightarrow & x = \frac{49}{102} & & \\ & V = \left\{ \frac{49}{102} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -14x+\frac{28}{9}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+308} & = & \color{red}{-495x} +90 \\\Leftrightarrow & -1386x \color{red}{+308} \color{blue}{-308} \color{blue}{+495x} & = & \color{red}{-495x} +90 \color{blue}{+495x} \color{blue}{-308} \\\Leftrightarrow & -1386x+495x& = & 90-308 \\\Leftrightarrow & \color{red}{-891} x& = & -218 \\\Leftrightarrow & x = \frac{-218}{-891} & & \\\Leftrightarrow & x = \frac{218}{891} & & \\ & V = \left\{ \frac{218}{891} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{-8} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -30x \color{red}{-8} \color{blue}{+8} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+8} \\\Leftrightarrow & -30x+21x& = & 2+8 \\\Leftrightarrow & \color{red}{-9} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-9} & & \\\Leftrightarrow & x = \frac{-10}{9} & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2025-12-19 20:06:56
Een site van Busleyden Atheneum Mechelen