Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +45 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +45 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 45-24 \\\Leftrightarrow & \color{red}{-70} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-70} & & \\\Leftrightarrow & x = \frac{-3}{10} & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & 8x+\frac{9}{4} \\\Leftrightarrow & 35x-\frac{35}{9}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x- \frac{140}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{-140} & = & \color{red}{288x} +81 \\\Leftrightarrow & 1260x \color{red}{-140} \color{blue}{+140} \color{blue}{-288x} & = & \color{red}{288x} +81 \color{blue}{-288x} \color{blue}{+140} \\\Leftrightarrow & 1260x-288x& = & 81+140 \\\Leftrightarrow & \color{red}{972} x& = & 221 \\\Leftrightarrow & x = \frac{221}{972} & & \\ & V = \left\{ \frac{221}{972} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{10})& = & 6x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{21}{10}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2450}{ \color{blue}{70} }x- \frac{147}{ \color{blue}{70} })& = & (\frac{420}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2450x \color{red}{-147} & = & \color{red}{420x} +100 \\\Leftrightarrow & -2450x \color{red}{-147} \color{blue}{+147} \color{blue}{-420x} & = & \color{red}{420x} +100 \color{blue}{-420x} \color{blue}{+147} \\\Leftrightarrow & -2450x-420x& = & 100+147 \\\Leftrightarrow & \color{red}{-2870} x& = & 247 \\\Leftrightarrow & x = \frac{247}{-2870} & & \\\Leftrightarrow & x = \frac{-247}{2870} & & \\ & V = \left\{ \frac{-247}{2870} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{480}{ \color{blue}{20} }x+ \frac{72}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 480x \color{red}{+72} & = & \color{red}{-140x} +15 \\\Leftrightarrow & 480x \color{red}{+72} \color{blue}{-72} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{-72} \\\Leftrightarrow & 480x+140x& = & 15-72 \\\Leftrightarrow & \color{red}{620} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{620} & & \\ & V = \left\{ \frac{-57}{620} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 9x+\frac{12}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+84} & = & \color{red}{-245x} +30 \\\Leftrightarrow & 315x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 315x+245x& = & 30-84 \\\Leftrightarrow & \color{red}{560} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{560} & & \\\Leftrightarrow & x = \frac{-27}{280} & & \\ & V = \left\{ \frac{-27}{280} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{99x} +88 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+30} \\\Leftrightarrow & 330x-99x& = & 88+30 \\\Leftrightarrow & \color{red}{231} x& = & 118 \\\Leftrightarrow & x = \frac{118}{231} & & \\ & V = \left\{ \frac{118}{231} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{4}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{-28} & = & \color{red}{245x} +50 \\\Leftrightarrow & 350x \color{red}{-28} \color{blue}{+28} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+28} \\\Leftrightarrow & 350x-245x& = & 50+28 \\\Leftrightarrow & \color{red}{105} x& = & 78 \\\Leftrightarrow & x = \frac{78}{105} & & \\\Leftrightarrow & x = \frac{26}{35} & & \\ & V = \left\{ \frac{26}{35} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3300}{ \color{blue}{110} }x+ \frac{180}{ \color{blue}{110} })& = & (\frac{-770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3300x \color{red}{+180} & = & \color{red}{-770x} +33 \\\Leftrightarrow & -3300x \color{red}{+180} \color{blue}{-180} \color{blue}{+770x} & = & \color{red}{-770x} +33 \color{blue}{+770x} \color{blue}{-180} \\\Leftrightarrow & -3300x+770x& = & 33-180 \\\Leftrightarrow & \color{red}{-2530} x& = & -147 \\\Leftrightarrow & x = \frac{-147}{-2530} & & \\\Leftrightarrow & x = \frac{147}{2530} & & \\ & V = \left\{ \frac{147}{2530} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 10x+\frac{6}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+30} & = & \color{red}{385x} +66 \\\Leftrightarrow & 550x \color{red}{+30} \color{blue}{-30} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{-30} \\\Leftrightarrow & 550x-385x& = & 66-30 \\\Leftrightarrow & \color{red}{165} x& = & 36 \\\Leftrightarrow & x = \frac{36}{165} & & \\\Leftrightarrow & x = \frac{12}{55} & & \\ & V = \left\{ \frac{12}{55} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{10})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x+\frac{9}{10}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-440}{ \color{blue}{110} }x+ \frac{20}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{+99} & = & \color{red}{-440x} +20 \\\Leftrightarrow & -1650x \color{red}{+99} \color{blue}{-99} \color{blue}{+440x} & = & \color{red}{-440x} +20 \color{blue}{+440x} \color{blue}{-99} \\\Leftrightarrow & -1650x+440x& = & 20-99 \\\Leftrightarrow & \color{red}{-1210} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-1210} & & \\\Leftrightarrow & x = \frac{79}{1210} & & \\ & V = \left\{ \frac{79}{1210} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{2}{7})& = & 4x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{6}{7}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{-54} & = & \color{red}{252x} +70 \\\Leftrightarrow & -945x \color{red}{-54} \color{blue}{+54} \color{blue}{-252x} & = & \color{red}{252x} +70 \color{blue}{-252x} \color{blue}{+54} \\\Leftrightarrow & -945x-252x& = & 70+54 \\\Leftrightarrow & \color{red}{-1197} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-1197} & & \\\Leftrightarrow & x = \frac{-124}{1197} & & \\ & V = \left\{ \frac{-124}{1197} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{210}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 210x \color{red}{+30} & = & \color{red}{49x} +3 \\\Leftrightarrow & 210x \color{red}{+30} \color{blue}{-30} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-30} \\\Leftrightarrow & 210x-49x& = & 3-30 \\\Leftrightarrow & \color{red}{161} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{161} & & \\ & V = \left\{ \frac{-27}{161} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-08-13 08:24:21
Een site van Busleyden Atheneum Mechelen