Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x-\frac{6}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-66} & = & \color{red}{539x} +14 \\\Leftrightarrow & -770x \color{red}{-66} \color{blue}{+66} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{+66} \\\Leftrightarrow & -770x-539x& = & 14+66 \\\Leftrightarrow & \color{red}{-1309} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-1309} & & \\\Leftrightarrow & x = \frac{-80}{1309} & & \\ & V = \left\{ \frac{-80}{1309} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{81x} +6 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +6 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & -72x-81x& = & 6-8 \\\Leftrightarrow & \color{red}{-153} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-153} & & \\\Leftrightarrow & x = \frac{2}{153} & & \\ & V = \left\{ \frac{2}{153} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{5})& = & 5x+\frac{5}{9} \\\Leftrightarrow & 18x-\frac{24}{5}& = & 5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{810}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 810x \color{red}{-216} & = & \color{red}{225x} +25 \\\Leftrightarrow & 810x \color{red}{-216} \color{blue}{+216} \color{blue}{-225x} & = & \color{red}{225x} +25 \color{blue}{-225x} \color{blue}{+216} \\\Leftrightarrow & 810x-225x& = & 25+216 \\\Leftrightarrow & \color{red}{585} x& = & 241 \\\Leftrightarrow & x = \frac{241}{585} & & \\ & V = \left\{ \frac{241}{585} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{9})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -16x+\frac{20}{9}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+20} & = & \color{red}{63x} +10 \\\Leftrightarrow & -144x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +10 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -144x-63x& = & 10-20 \\\Leftrightarrow & \color{red}{-207} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-207} & & \\\Leftrightarrow & x = \frac{10}{207} & & \\ & V = \left\{ \frac{10}{207} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{7})& = & 2x+\frac{5}{9} \\\Leftrightarrow & 15x+\frac{25}{7}& = & 2x+\frac{5}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x+ \frac{225}{ \color{blue}{63} })& = & (\frac{126}{ \color{blue}{63} }x+ \frac{35}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{+225} & = & \color{red}{126x} +35 \\\Leftrightarrow & 945x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +35 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & 945x-126x& = & 35-225 \\\Leftrightarrow & \color{red}{819} x& = & -190 \\\Leftrightarrow & x = \frac{-190}{819} & & \\ & V = \left\{ \frac{-190}{819} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-56} & = & \color{red}{-147x} +12 \\\Leftrightarrow & -420x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +12 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & -420x+147x& = & 12+56 \\\Leftrightarrow & \color{red}{-273} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-273} & & \\\Leftrightarrow & x = \frac{-68}{273} & & \\ & V = \left\{ \frac{-68}{273} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{2})& = & 9x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{25}{2}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{+125} & = & \color{red}{90x} +8 \\\Leftrightarrow & 200x \color{red}{+125} \color{blue}{-125} \color{blue}{-90x} & = & \color{red}{90x} +8 \color{blue}{-90x} \color{blue}{-125} \\\Leftrightarrow & 200x-90x& = & 8-125 \\\Leftrightarrow & \color{red}{110} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{110} & & \\ & V = \left\{ \frac{-117}{110} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{11})& = & -3x+\frac{8}{5} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -3x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+40} \\\Leftrightarrow & 440x+165x& = & 88+40 \\\Leftrightarrow & \color{red}{605} x& = & 128 \\\Leftrightarrow & x = \frac{128}{605} & & \\ & V = \left\{ \frac{128}{605} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{6})& = & -6x+\frac{6}{5} \\\Leftrightarrow & -35x+\frac{35}{6}& = & -6x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x+ \frac{175}{ \color{blue}{30} })& = & (\frac{-180}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{+175} & = & \color{red}{-180x} +36 \\\Leftrightarrow & -1050x \color{red}{+175} \color{blue}{-175} \color{blue}{+180x} & = & \color{red}{-180x} +36 \color{blue}{+180x} \color{blue}{-175} \\\Leftrightarrow & -1050x+180x& = & 36-175 \\\Leftrightarrow & \color{red}{-870} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-870} & & \\\Leftrightarrow & x = \frac{139}{870} & & \\ & V = \left\{ \frac{139}{870} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{3})& = & -8x+\frac{4}{7} \\\Leftrightarrow & 35x+\frac{28}{3}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{735}{ \color{blue}{21} }x+ \frac{196}{ \color{blue}{21} })& = & (\frac{-168}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 735x \color{red}{+196} & = & \color{red}{-168x} +12 \\\Leftrightarrow & 735x \color{red}{+196} \color{blue}{-196} \color{blue}{+168x} & = & \color{red}{-168x} +12 \color{blue}{+168x} \color{blue}{-196} \\\Leftrightarrow & 735x+168x& = & 12-196 \\\Leftrightarrow & \color{red}{903} x& = & -184 \\\Leftrightarrow & x = \frac{-184}{903} & & \\ & V = \left\{ \frac{-184}{903} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{4}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 15x+\frac{20}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+100} & = & \color{red}{-385x} +77 \\\Leftrightarrow & 825x \color{red}{+100} \color{blue}{-100} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{-100} \\\Leftrightarrow & 825x+385x& = & 77-100 \\\Leftrightarrow & \color{red}{1210} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{1210} & & \\ & V = \left\{ \frac{-23}{1210} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x-\frac{15}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-30} & = & \color{red}{98x} +49 \\\Leftrightarrow & -140x \color{red}{-30} \color{blue}{+30} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{+30} \\\Leftrightarrow & -140x-98x& = & 49+30 \\\Leftrightarrow & \color{red}{-238} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-238} & & \\\Leftrightarrow & x = \frac{-79}{238} & & \\ & V = \left\{ \frac{-79}{238} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-29 19:51:30
Een site van Busleyden Atheneum Mechelen