Vgln. eerste graad (reeks 5)

Hoofdmenu Eentje per keer 

Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x+\frac{6}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+66} & = & \color{red}{539x} +70 \\\Leftrightarrow & -770x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -770x-539x& = & 70-66 \\\Leftrightarrow & \color{red}{-1309} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-1309} & & \\\Leftrightarrow & x = \frac{-4}{1309} & & \\ & V = \left\{ \frac{-4}{1309} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-66} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -770x \color{red}{-66} \color{blue}{+66} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+66} \\\Leftrightarrow & -770x+539x& = & 42+66 \\\Leftrightarrow & \color{red}{-231} x& = & 108 \\\Leftrightarrow & x = \frac{108}{-231} & & \\\Leftrightarrow & x = \frac{-36}{77} & & \\ & V = \left\{ \frac{-36}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{-135x} +20 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +20 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -300x+135x& = & 20+36 \\\Leftrightarrow & \color{red}{-165} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-165} & & \\\Leftrightarrow & x = \frac{-56}{165} & & \\ & V = \left\{ \frac{-56}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{5}{4})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+135} & = & \color{red}{-180x} +8 \\\Leftrightarrow & -432x \color{red}{+135} \color{blue}{-135} \color{blue}{+180x} & = & \color{red}{-180x} +8 \color{blue}{+180x} \color{blue}{-135} \\\Leftrightarrow & -432x+180x& = & 8-135 \\\Leftrightarrow & \color{red}{-252} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-252} & & \\\Leftrightarrow & x = \frac{127}{252} & & \\ & V = \left\{ \frac{127}{252} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{441x} +14 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{+90} \\\Leftrightarrow & 630x-441x& = & 14+90 \\\Leftrightarrow & \color{red}{189} x& = & 104 \\\Leftrightarrow & x = \frac{104}{189} & & \\ & V = \left\{ \frac{104}{189} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{-36} & = & \color{red}{120x} +50 \\\Leftrightarrow & -270x \color{red}{-36} \color{blue}{+36} \color{blue}{-120x} & = & \color{red}{120x} +50 \color{blue}{-120x} \color{blue}{+36} \\\Leftrightarrow & -270x-120x& = & 50+36 \\\Leftrightarrow & \color{red}{-390} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-390} & & \\\Leftrightarrow & x = \frac{-43}{195} & & \\ & V = \left\{ \frac{-43}{195} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{11})& = & -8x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{11}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+45} & = & \color{red}{-264x} +44 \\\Leftrightarrow & 495x \color{red}{+45} \color{blue}{-45} \color{blue}{+264x} & = & \color{red}{-264x} +44 \color{blue}{+264x} \color{blue}{-45} \\\Leftrightarrow & 495x+264x& = & 44-45 \\\Leftrightarrow & \color{red}{759} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{759} & & \\ & V = \left\{ \frac{-1}{759} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{5})& = & -9x+\frac{7}{5} \\\Leftrightarrow & -4x+\frac{4}{5}& = & -9x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -20x \color{red}{+4} & = & \color{red}{-45x} +7 \\\Leftrightarrow & -20x \color{red}{+4} \color{blue}{-4} \color{blue}{+45x} & = & \color{red}{-45x} +7 \color{blue}{+45x} \color{blue}{-4} \\\Leftrightarrow & -20x+45x& = & 7-4 \\\Leftrightarrow & \color{red}{25} x& = & 3 \\\Leftrightarrow & x = \frac{3}{25} & & \\ & V = \left\{ \frac{3}{25} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{7})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 20x-\frac{15}{7}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{165}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-165} & = & \color{red}{-693x} +70 \\\Leftrightarrow & 1540x \color{red}{-165} \color{blue}{+165} \color{blue}{+693x} & = & \color{red}{-693x} +70 \color{blue}{+693x} \color{blue}{+165} \\\Leftrightarrow & 1540x+693x& = & 70+165 \\\Leftrightarrow & \color{red}{2233} x& = & 235 \\\Leftrightarrow & x = \frac{235}{2233} & & \\ & V = \left\{ \frac{235}{2233} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{11})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 21x+\frac{14}{11}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x+ \frac{112}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{+112} & = & \color{red}{440x} +77 \\\Leftrightarrow & 1848x \color{red}{+112} \color{blue}{-112} \color{blue}{-440x} & = & \color{red}{440x} +77 \color{blue}{-440x} \color{blue}{-112} \\\Leftrightarrow & 1848x-440x& = & 77-112 \\\Leftrightarrow & \color{red}{1408} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{1408} & & \\ & V = \left\{ \frac{-35}{1408} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{4})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 10x+\frac{25}{4}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{280}{ \color{blue}{28} }x+ \frac{175}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 280x \color{red}{+175} & = & \color{red}{-84x} +8 \\\Leftrightarrow & 280x \color{red}{+175} \color{blue}{-175} \color{blue}{+84x} & = & \color{red}{-84x} +8 \color{blue}{+84x} \color{blue}{-175} \\\Leftrightarrow & 280x+84x& = & 8-175 \\\Leftrightarrow & \color{red}{364} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{364} & & \\ & V = \left\{ \frac{-167}{364} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 42+110 \\\Leftrightarrow & \color{red}{-231} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-231} & & \\\Leftrightarrow & x = \frac{-152}{231} & & \\ & V = \left\{ \frac{-152}{231} \right\} & \\\end{align}\)
Oefeningengenerator wiskundeoefeningen.be 2026-01-09 09:35:46
Een site van Busleyden Atheneum Mechelen