Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+56} & = & \color{red}{189x} +6 \\\Leftrightarrow & 168x \color{red}{+56} \color{blue}{-56} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{-56} \\\Leftrightarrow & 168x-189x& = & 6-56 \\\Leftrightarrow & \color{red}{-21} x& = & -50 \\\Leftrightarrow & x = \frac{-50}{-21} & & \\\Leftrightarrow & x = \frac{50}{21} & & \\ & V = \left\{ \frac{50}{21} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{2}{7})& = & 4x+\frac{10}{11} \\\Leftrightarrow & -15x+\frac{10}{7}& = & 4x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+110} & = & \color{red}{308x} +70 \\\Leftrightarrow & -1155x \color{red}{+110} \color{blue}{-110} \color{blue}{-308x} & = & \color{red}{308x} +70 \color{blue}{-308x} \color{blue}{-110} \\\Leftrightarrow & -1155x-308x& = & 70-110 \\\Leftrightarrow & \color{red}{-1463} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-1463} & & \\\Leftrightarrow & x = \frac{40}{1463} & & \\ & V = \left\{ \frac{40}{1463} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & -4x+\frac{5}{2} \\\Leftrightarrow & 21x-\frac{14}{3}& = & -4x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{126}{ \color{blue}{6} }x- \frac{28}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{-24x} +15 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{+24x} & = & \color{red}{-24x} +15 \color{blue}{+24x} \color{blue}{+28} \\\Leftrightarrow & 126x+24x& = & 15+28 \\\Leftrightarrow & \color{red}{150} x& = & 43 \\\Leftrightarrow & x = \frac{43}{150} & & \\ & V = \left\{ \frac{43}{150} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 7x+\frac{7}{8} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-800}{ \color{blue}{40} }x+ \frac{96}{ \color{blue}{40} })& = & (\frac{280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -800x \color{red}{+96} & = & \color{red}{280x} +35 \\\Leftrightarrow & -800x \color{red}{+96} \color{blue}{-96} \color{blue}{-280x} & = & \color{red}{280x} +35 \color{blue}{-280x} \color{blue}{-96} \\\Leftrightarrow & -800x-280x& = & 35-96 \\\Leftrightarrow & \color{red}{-1080} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1080} & & \\\Leftrightarrow & x = \frac{61}{1080} & & \\ & V = \left\{ \frac{61}{1080} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{2}{3})& = & 9x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{8}{3}& = & 9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-88} & = & \color{red}{297x} +15 \\\Leftrightarrow & 264x \color{red}{-88} \color{blue}{+88} \color{blue}{-297x} & = & \color{red}{297x} +15 \color{blue}{-297x} \color{blue}{+88} \\\Leftrightarrow & 264x-297x& = & 15+88 \\\Leftrightarrow & \color{red}{-33} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-33} & & \\\Leftrightarrow & x = \frac{-103}{33} & & \\ & V = \left\{ \frac{-103}{33} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & -4x+\frac{9}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -4x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-140x} +63 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+140x} & = & \color{red}{-140x} +63 \color{blue}{+140x} \color{blue}{+150} \\\Leftrightarrow & -630x+140x& = & 63+150 \\\Leftrightarrow & \color{red}{-490} x& = & 213 \\\Leftrightarrow & x = \frac{213}{-490} & & \\\Leftrightarrow & x = \frac{-213}{490} & & \\ & V = \left\{ \frac{-213}{490} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 3x+\frac{4}{11} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-132} & = & \color{red}{165x} +20 \\\Leftrightarrow & -990x \color{red}{-132} \color{blue}{+132} \color{blue}{-165x} & = & \color{red}{165x} +20 \color{blue}{-165x} \color{blue}{+132} \\\Leftrightarrow & -990x-165x& = & 20+132 \\\Leftrightarrow & \color{red}{-1155} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-1155} & & \\\Leftrightarrow & x = \frac{-152}{1155} & & \\ & V = \left\{ \frac{-152}{1155} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{4}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x-\frac{8}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-88} & = & \color{red}{385x} +42 \\\Leftrightarrow & 462x \color{red}{-88} \color{blue}{+88} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+88} \\\Leftrightarrow & 462x-385x& = & 42+88 \\\Leftrightarrow & \color{red}{77} x& = & 130 \\\Leftrightarrow & x = \frac{130}{77} & & \\ & V = \left\{ \frac{130}{77} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{8}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{+24} & = & \color{red}{231x} +88 \\\Leftrightarrow & 330x \color{red}{+24} \color{blue}{-24} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-24} \\\Leftrightarrow & 330x-231x& = & 88-24 \\\Leftrightarrow & \color{red}{99} x& = & 64 \\\Leftrightarrow & x = \frac{64}{99} & & \\ & V = \left\{ \frac{64}{99} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-132} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -330x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -330x+385x& = & 30+132 \\\Leftrightarrow & \color{red}{55} x& = & 162 \\\Leftrightarrow & x = \frac{162}{55} & & \\ & V = \left\{ \frac{162}{55} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{11})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 28x-\frac{21}{11}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x- \frac{84}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{-84} & = & \color{red}{-220x} +99 \\\Leftrightarrow & 1232x \color{red}{-84} \color{blue}{+84} \color{blue}{+220x} & = & \color{red}{-220x} +99 \color{blue}{+220x} \color{blue}{+84} \\\Leftrightarrow & 1232x+220x& = & 99+84 \\\Leftrightarrow & \color{red}{1452} x& = & 183 \\\Leftrightarrow & x = \frac{183}{1452} & & \\\Leftrightarrow & x = \frac{61}{484} & & \\ & V = \left\{ \frac{61}{484} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{4}{9})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{20}{9}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-20} & = & \color{red}{63x} +4 \\\Leftrightarrow & -90x \color{red}{-20} \color{blue}{+20} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+20} \\\Leftrightarrow & -90x-63x& = & 4+20 \\\Leftrightarrow & \color{red}{-153} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-153} & & \\\Leftrightarrow & x = \frac{-8}{51} & & \\ & V = \left\{ \frac{-8}{51} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-29 14:30:51
Een site van Busleyden Atheneum Mechelen