Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{3})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{35}{3}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-693}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -693x \color{red}{+385} & = & \color{red}{264x} +18 \\\Leftrightarrow & -693x \color{red}{+385} \color{blue}{-385} \color{blue}{-264x} & = & \color{red}{264x} +18 \color{blue}{-264x} \color{blue}{-385} \\\Leftrightarrow & -693x-264x& = & 18-385 \\\Leftrightarrow & \color{red}{-957} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-957} & & \\\Leftrightarrow & x = \frac{367}{957} & & \\ & V = \left\{ \frac{367}{957} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & -5x+\frac{4}{7} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{-105x} +12 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{+105x} & = & \color{red}{-105x} +12 \color{blue}{+105x} \color{blue}{-56} \\\Leftrightarrow & 252x+105x& = & 12-56 \\\Leftrightarrow & \color{red}{357} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{357} & & \\ & V = \left\{ \frac{-44}{357} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -25x+\frac{10}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{+20} & = & \color{red}{-126x} +81 \\\Leftrightarrow & -450x \color{red}{+20} \color{blue}{-20} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-20} \\\Leftrightarrow & -450x+126x& = & 81-20 \\\Leftrightarrow & \color{red}{-324} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-324} & & \\\Leftrightarrow & x = \frac{-61}{324} & & \\ & V = \left\{ \frac{-61}{324} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+330} & = & \color{red}{-385x} +63 \\\Leftrightarrow & -924x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +63 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & -924x+385x& = & 63-330 \\\Leftrightarrow & \color{red}{-539} x& = & -267 \\\Leftrightarrow & x = \frac{-267}{-539} & & \\\Leftrightarrow & x = \frac{267}{539} & & \\ & V = \left\{ \frac{267}{539} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{9})& = & -9x+\frac{3}{7} \\\Leftrightarrow & -28x+\frac{28}{9}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{+196} & = & \color{red}{-567x} +27 \\\Leftrightarrow & -1764x \color{red}{+196} \color{blue}{-196} \color{blue}{+567x} & = & \color{red}{-567x} +27 \color{blue}{+567x} \color{blue}{-196} \\\Leftrightarrow & -1764x+567x& = & 27-196 \\\Leftrightarrow & \color{red}{-1197} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-1197} & & \\\Leftrightarrow & x = \frac{169}{1197} & & \\ & V = \left\{ \frac{169}{1197} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{4}{11})& = & 2x+\frac{8}{3} \\\Leftrightarrow & -18x-\frac{24}{11}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-594}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -594x \color{red}{-72} & = & \color{red}{66x} +88 \\\Leftrightarrow & -594x \color{red}{-72} \color{blue}{+72} \color{blue}{-66x} & = & \color{red}{66x} +88 \color{blue}{-66x} \color{blue}{+72} \\\Leftrightarrow & -594x-66x& = & 88+72 \\\Leftrightarrow & \color{red}{-660} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-660} & & \\\Leftrightarrow & x = \frac{-8}{33} & & \\ & V = \left\{ \frac{-8}{33} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{5}{7})& = & 5x+\frac{2}{7} \\\Leftrightarrow & 24x+\frac{30}{7}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{168}{ \color{blue}{7} }x+ \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 168x \color{red}{+30} & = & \color{red}{35x} +2 \\\Leftrightarrow & 168x \color{red}{+30} \color{blue}{-30} \color{blue}{-35x} & = & \color{red}{35x} +2 \color{blue}{-35x} \color{blue}{-30} \\\Leftrightarrow & 168x-35x& = & 2-30 \\\Leftrightarrow & \color{red}{133} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{133} & & \\\Leftrightarrow & x = \frac{-4}{19} & & \\ & V = \left\{ \frac{-4}{19} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -10x+\frac{8}{9}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-360}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -360x \color{red}{+32} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -360x \color{red}{+32} \color{blue}{-32} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-32} \\\Leftrightarrow & -360x+252x& = & 21-32 \\\Leftrightarrow & \color{red}{-108} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-108} & & \\\Leftrightarrow & x = \frac{11}{108} & & \\ & V = \left\{ \frac{11}{108} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{4})& = & 2x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{25}{4}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{75}{ \color{blue}{12} })& = & (\frac{24}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+75} & = & \color{red}{24x} +40 \\\Leftrightarrow & 180x \color{red}{+75} \color{blue}{-75} \color{blue}{-24x} & = & \color{red}{24x} +40 \color{blue}{-24x} \color{blue}{-75} \\\Leftrightarrow & 180x-24x& = & 40-75 \\\Leftrightarrow & \color{red}{156} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{156} & & \\ & V = \left\{ \frac{-35}{156} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{3})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 21x+\frac{28}{3}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{63}{ \color{blue}{3} }x+ \frac{28}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 63x \color{red}{+28} & = & \color{red}{6x} +2 \\\Leftrightarrow & 63x \color{red}{+28} \color{blue}{-28} \color{blue}{-6x} & = & \color{red}{6x} +2 \color{blue}{-6x} \color{blue}{-28} \\\Leftrightarrow & 63x-6x& = & 2-28 \\\Leftrightarrow & \color{red}{57} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{57} & & \\ & V = \left\{ \frac{-26}{57} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{4})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -35x+\frac{21}{4}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-980}{ \color{blue}{28} }x+ \frac{147}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -980x \color{red}{+147} & = & \color{red}{252x} +8 \\\Leftrightarrow & -980x \color{red}{+147} \color{blue}{-147} \color{blue}{-252x} & = & \color{red}{252x} +8 \color{blue}{-252x} \color{blue}{-147} \\\Leftrightarrow & -980x-252x& = & 8-147 \\\Leftrightarrow & \color{red}{-1232} x& = & -139 \\\Leftrightarrow & x = \frac{-139}{-1232} & & \\\Leftrightarrow & x = \frac{139}{1232} & & \\ & V = \left\{ \frac{139}{1232} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-132} & = & \color{red}{-220x} +30 \\\Leftrightarrow & -825x \color{red}{-132} \color{blue}{+132} \color{blue}{+220x} & = & \color{red}{-220x} +30 \color{blue}{+220x} \color{blue}{+132} \\\Leftrightarrow & -825x+220x& = & 30+132 \\\Leftrightarrow & \color{red}{-605} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-605} & & \\\Leftrightarrow & x = \frac{-162}{605} & & \\ & V = \left\{ \frac{-162}{605} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-07-16 09:12:59
Een site van Busleyden Atheneum Mechelen