Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{245x} +25 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{-245x} & = & \color{red}{245x} +25 \color{blue}{-245x} \color{blue}{+28} \\\Leftrightarrow & 140x-245x& = & 25+28 \\\Leftrightarrow & \color{red}{-105} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-105} & & \\\Leftrightarrow & x = \frac{-53}{105} & & \\ & V = \left\{ \frac{-53}{105} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{385x} +10 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1650x-385x& = & 10+264 \\\Leftrightarrow & \color{red}{1265} x& = & 274 \\\Leftrightarrow & x = \frac{274}{1265} & & \\ & V = \left\{ \frac{274}{1265} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{9}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+27} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -252x \color{red}{+27} \color{blue}{-27} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-27} \\\Leftrightarrow & -252x+105x& = & 70-27 \\\Leftrightarrow & \color{red}{-147} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-147} & & \\\Leftrightarrow & x = \frac{-43}{147} & & \\ & V = \left\{ \frac{-43}{147} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{7})& = & 7x+\frac{7}{11} \\\Leftrightarrow & -10x+\frac{10}{7}& = & 7x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+110} & = & \color{red}{539x} +49 \\\Leftrightarrow & -770x \color{red}{+110} \color{blue}{-110} \color{blue}{-539x} & = & \color{red}{539x} +49 \color{blue}{-539x} \color{blue}{-110} \\\Leftrightarrow & -770x-539x& = & 49-110 \\\Leftrightarrow & \color{red}{-1309} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1309} & & \\\Leftrightarrow & x = \frac{61}{1309} & & \\ & V = \left\{ \frac{61}{1309} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{-24} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -180x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & -180x+90x& = & 45+24 \\\Leftrightarrow & \color{red}{-90} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-90} & & \\\Leftrightarrow & x = \frac{-23}{30} & & \\ & V = \left\{ \frac{-23}{30} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & 8x+\frac{4}{3} \\\Leftrightarrow & 35x-\frac{14}{3}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{14}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-14} & = & \color{red}{24x} +4 \\\Leftrightarrow & 105x \color{red}{-14} \color{blue}{+14} \color{blue}{-24x} & = & \color{red}{24x} +4 \color{blue}{-24x} \color{blue}{+14} \\\Leftrightarrow & 105x-24x& = & 4+14 \\\Leftrightarrow & \color{red}{81} x& = & 18 \\\Leftrightarrow & x = \frac{18}{81} & & \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{8})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 15x-\frac{25}{8}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x- \frac{125}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{56}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{-125} & = & \color{red}{-280x} +56 \\\Leftrightarrow & 600x \color{red}{-125} \color{blue}{+125} \color{blue}{+280x} & = & \color{red}{-280x} +56 \color{blue}{+280x} \color{blue}{+125} \\\Leftrightarrow & 600x+280x& = & 56+125 \\\Leftrightarrow & \color{red}{880} x& = & 181 \\\Leftrightarrow & x = \frac{181}{880} & & \\ & V = \left\{ \frac{181}{880} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{4}{7})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 20x+\frac{16}{7}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{140}{ \color{blue}{7} }x+ \frac{16}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 140x \color{red}{+16} & = & \color{red}{-49x} +2 \\\Leftrightarrow & 140x \color{red}{+16} \color{blue}{-16} \color{blue}{+49x} & = & \color{red}{-49x} +2 \color{blue}{+49x} \color{blue}{-16} \\\Leftrightarrow & 140x+49x& = & 2-16 \\\Leftrightarrow & \color{red}{189} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{189} & & \\\Leftrightarrow & x = \frac{-2}{27} & & \\ & V = \left\{ \frac{-2}{27} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{11})& = & 9x+\frac{4}{9} \\\Leftrightarrow & 16x+\frac{12}{11}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1584}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1584x \color{red}{+108} & = & \color{red}{891x} +44 \\\Leftrightarrow & 1584x \color{red}{+108} \color{blue}{-108} \color{blue}{-891x} & = & \color{red}{891x} +44 \color{blue}{-891x} \color{blue}{-108} \\\Leftrightarrow & 1584x-891x& = & 44-108 \\\Leftrightarrow & \color{red}{693} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{693} & & \\ & V = \left\{ \frac{-64}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{300}{ \color{blue}{10} }x- \frac{48}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 300x \color{red}{-48} & = & \color{red}{-70x} +15 \\\Leftrightarrow & 300x \color{red}{-48} \color{blue}{+48} \color{blue}{+70x} & = & \color{red}{-70x} +15 \color{blue}{+70x} \color{blue}{+48} \\\Leftrightarrow & 300x+70x& = & 15+48 \\\Leftrightarrow & \color{red}{370} x& = & 63 \\\Leftrightarrow & x = \frac{63}{370} & & \\ & V = \left\{ \frac{63}{370} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-330} & = & \color{red}{385x} +42 \\\Leftrightarrow & 1386x \color{red}{-330} \color{blue}{+330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+330} \\\Leftrightarrow & 1386x-385x& = & 42+330 \\\Leftrightarrow & \color{red}{1001} x& = & 372 \\\Leftrightarrow & x = \frac{372}{1001} & & \\ & V = \left\{ \frac{372}{1001} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{4}{11})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 14x-\frac{28}{11}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{196}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-196} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 1078x \color{red}{-196} \color{blue}{+196} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+196} \\\Leftrightarrow & 1078x+385x& = & 66+196 \\\Leftrightarrow & \color{red}{1463} x& = & 262 \\\Leftrightarrow & x = \frac{262}{1463} & & \\ & V = \left\{ \frac{262}{1463} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-09-19 09:24:46
Een site van Busleyden Atheneum Mechelen