Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{5}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-30} & = & \color{red}{40x} +5 \\\Leftrightarrow & -96x \color{red}{-30} \color{blue}{+30} \color{blue}{-40x} & = & \color{red}{40x} +5 \color{blue}{-40x} \color{blue}{+30} \\\Leftrightarrow & -96x-40x& = & 5+30 \\\Leftrightarrow & \color{red}{-136} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-136} & & \\\Leftrightarrow & x = \frac{-35}{136} & & \\ & V = \left\{ \frac{-35}{136} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-35x} +7 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+35x} & = & \color{red}{-35x} +7 \color{blue}{+35x} \color{blue}{-24} \\\Leftrightarrow & 90x+35x& = & 7-24 \\\Leftrightarrow & \color{red}{125} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{125} & & \\ & V = \left\{ \frac{-17}{125} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{3}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-126} & = & \color{red}{385x} +33 \\\Leftrightarrow & 1848x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & 1848x-385x& = & 33+126 \\\Leftrightarrow & \color{red}{1463} x& = & 159 \\\Leftrightarrow & x = \frac{159}{1463} & & \\ & V = \left\{ \frac{159}{1463} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{5})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{16}{5}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{48}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{75x} +40 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{-75x} & = & \color{red}{75x} +40 \color{blue}{-75x} \color{blue}{-48} \\\Leftrightarrow & -180x-75x& = & 40-48 \\\Leftrightarrow & \color{red}{-255} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-255} & & \\\Leftrightarrow & x = \frac{8}{255} & & \\ & V = \left\{ \frac{8}{255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 6x+\frac{8}{9}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{108}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{27}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 108x \color{red}{+16} & = & \color{red}{-90x} +27 \\\Leftrightarrow & 108x \color{red}{+16} \color{blue}{-16} \color{blue}{+90x} & = & \color{red}{-90x} +27 \color{blue}{+90x} \color{blue}{-16} \\\Leftrightarrow & 108x+90x& = & 27-16 \\\Leftrightarrow & \color{red}{198} x& = & 11 \\\Leftrightarrow & x = \frac{11}{198} & & \\\Leftrightarrow & x = \frac{1}{18} & & \\ & V = \left\{ \frac{1}{18} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{2}{3})& = & 8x+\frac{6}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{120x} +18 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +18 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & 315x-120x& = & 18-70 \\\Leftrightarrow & \color{red}{195} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{195} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & 7x+\frac{9}{5} \\\Leftrightarrow & 30x-\frac{18}{5}& = & 7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{35x} +9 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{-35x} & = & \color{red}{35x} +9 \color{blue}{-35x} \color{blue}{+18} \\\Leftrightarrow & 150x-35x& = & 9+18 \\\Leftrightarrow & \color{red}{115} x& = & 27 \\\Leftrightarrow & x = \frac{27}{115} & & \\ & V = \left\{ \frac{27}{115} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{5}{4})& = & -8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{-75} & = & \color{red}{-160x} +24 \\\Leftrightarrow & -300x \color{red}{-75} \color{blue}{+75} \color{blue}{+160x} & = & \color{red}{-160x} +24 \color{blue}{+160x} \color{blue}{+75} \\\Leftrightarrow & -300x+160x& = & 24+75 \\\Leftrightarrow & \color{red}{-140} x& = & 99 \\\Leftrightarrow & x = \frac{99}{-140} & & \\\Leftrightarrow & x = \frac{-99}{140} & & \\ & V = \left\{ \frac{-99}{140} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{9})& = & 3x+\frac{7}{11} \\\Leftrightarrow & 25x-\frac{10}{9}& = & 3x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{-110} & = & \color{red}{297x} +63 \\\Leftrightarrow & 2475x \color{red}{-110} \color{blue}{+110} \color{blue}{-297x} & = & \color{red}{297x} +63 \color{blue}{-297x} \color{blue}{+110} \\\Leftrightarrow & 2475x-297x& = & 63+110 \\\Leftrightarrow & \color{red}{2178} x& = & 173 \\\Leftrightarrow & x = \frac{173}{2178} & & \\ & V = \left\{ \frac{173}{2178} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 450x \color{red}{-36} & = & \color{red}{105x} +50 \\\Leftrightarrow & 450x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & 450x-105x& = & 50+36 \\\Leftrightarrow & \color{red}{345} x& = & 86 \\\Leftrightarrow & x = \frac{86}{345} & & \\ & V = \left\{ \frac{86}{345} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{3})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-140} & = & \color{red}{-147x} +24 \\\Leftrightarrow & 210x \color{red}{-140} \color{blue}{+140} \color{blue}{+147x} & = & \color{red}{-147x} +24 \color{blue}{+147x} \color{blue}{+140} \\\Leftrightarrow & 210x+147x& = & 24+140 \\\Leftrightarrow & \color{red}{357} x& = & 164 \\\Leftrightarrow & x = \frac{164}{357} & & \\ & V = \left\{ \frac{164}{357} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & -9x+\frac{10}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & -9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{-189x} +30 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{+189x} & = & \color{red}{-189x} +30 \color{blue}{+189x} \color{blue}{+98} \\\Leftrightarrow & 588x+189x& = & 30+98 \\\Leftrightarrow & \color{red}{777} x& = & 128 \\\Leftrightarrow & x = \frac{128}{777} & & \\ & V = \left\{ \frac{128}{777} \right\} & \\\end{align}\)
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