Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{3}{8})& = & 6x+\frac{9}{7} \\\Leftrightarrow & -25x+\frac{15}{8}& = & 6x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1400}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{336}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{336x} +72 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{-336x} & = & \color{red}{336x} +72 \color{blue}{-336x} \color{blue}{-105} \\\Leftrightarrow & -1400x-336x& = & 72-105 \\\Leftrightarrow & \color{red}{-1736} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-1736} & & \\\Leftrightarrow & x = \frac{33}{1736} & & \\ & V = \left\{ \frac{33}{1736} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{4}{3})& = & -3x+\frac{3}{5} \\\Leftrightarrow & 28x-\frac{28}{3}& = & -3x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{420}{ \color{blue}{15} }x- \frac{140}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 420x \color{red}{-140} & = & \color{red}{-45x} +9 \\\Leftrightarrow & 420x \color{red}{-140} \color{blue}{+140} \color{blue}{+45x} & = & \color{red}{-45x} +9 \color{blue}{+45x} \color{blue}{+140} \\\Leftrightarrow & 420x+45x& = & 9+140 \\\Leftrightarrow & \color{red}{465} x& = & 149 \\\Leftrightarrow & x = \frac{149}{465} & & \\ & V = \left\{ \frac{149}{465} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 6x+\frac{10}{7} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+126} & = & \color{red}{462x} +110 \\\Leftrightarrow & -1386x \color{red}{+126} \color{blue}{-126} \color{blue}{-462x} & = & \color{red}{462x} +110 \color{blue}{-462x} \color{blue}{-126} \\\Leftrightarrow & -1386x-462x& = & 110-126 \\\Leftrightarrow & \color{red}{-1848} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1848} & & \\\Leftrightarrow & x = \frac{2}{231} & & \\ & V = \left\{ \frac{2}{231} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{135x} +24 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-135x} & = & \color{red}{135x} +24 \color{blue}{-135x} \color{blue}{+40} \\\Leftrightarrow & -120x-135x& = & 24+40 \\\Leftrightarrow & \color{red}{-255} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-255} & & \\\Leftrightarrow & x = \frac{-64}{255} & & \\ & V = \left\{ \frac{-64}{255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -9x+\frac{7}{12} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -9x+\frac{7}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{14}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-216x} +14 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+216x} & = & \color{red}{-216x} +14 \color{blue}{+216x} \color{blue}{-63} \\\Leftrightarrow & -672x+216x& = & 14-63 \\\Leftrightarrow & \color{red}{-456} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{-456} & & \\\Leftrightarrow & x = \frac{49}{456} & & \\ & V = \left\{ \frac{49}{456} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{9})& = & 3x+\frac{7}{8} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x- \frac{280}{ \color{blue}{72} })& = & (\frac{216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{-280} & = & \color{red}{216x} +63 \\\Leftrightarrow & -2520x \color{red}{-280} \color{blue}{+280} \color{blue}{-216x} & = & \color{red}{216x} +63 \color{blue}{-216x} \color{blue}{+280} \\\Leftrightarrow & -2520x-216x& = & 63+280 \\\Leftrightarrow & \color{red}{-2736} x& = & 343 \\\Leftrightarrow & x = \frac{343}{-2736} & & \\\Leftrightarrow & x = \frac{-343}{2736} & & \\ & V = \left\{ \frac{-343}{2736} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{8}{5} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{100x} +32 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{-100x} & = & \color{red}{100x} +32 \color{blue}{-100x} \color{blue}{+75} \\\Leftrightarrow & -240x-100x& = & 32+75 \\\Leftrightarrow & \color{red}{-340} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-340} & & \\\Leftrightarrow & x = \frac{-107}{340} & & \\ & V = \left\{ \frac{-107}{340} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{7})& = & 5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{7}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+48} & = & \color{red}{105x} +28 \\\Leftrightarrow & -252x \color{red}{+48} \color{blue}{-48} \color{blue}{-105x} & = & \color{red}{105x} +28 \color{blue}{-105x} \color{blue}{-48} \\\Leftrightarrow & -252x-105x& = & 28-48 \\\Leftrightarrow & \color{red}{-357} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-357} & & \\\Leftrightarrow & x = \frac{20}{357} & & \\ & V = \left\{ \frac{20}{357} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 9x+\frac{15}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x+ \frac{45}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{+45} & = & \color{red}{231x} +88 \\\Leftrightarrow & 297x \color{red}{+45} \color{blue}{-45} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-45} \\\Leftrightarrow & 297x-231x& = & 88-45 \\\Leftrightarrow & \color{red}{66} x& = & 43 \\\Leftrightarrow & x = \frac{43}{66} & & \\ & V = \left\{ \frac{43}{66} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-36} & = & \color{red}{45x} +50 \\\Leftrightarrow & 120x \color{red}{-36} \color{blue}{+36} \color{blue}{-45x} & = & \color{red}{45x} +50 \color{blue}{-45x} \color{blue}{+36} \\\Leftrightarrow & 120x-45x& = & 50+36 \\\Leftrightarrow & \color{red}{75} x& = & 86 \\\Leftrightarrow & x = \frac{86}{75} & & \\ & V = \left\{ \frac{86}{75} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-60}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{-36} & = & \color{red}{-60x} +40 \\\Leftrightarrow & -225x \color{red}{-36} \color{blue}{+36} \color{blue}{+60x} & = & \color{red}{-60x} +40 \color{blue}{+60x} \color{blue}{+36} \\\Leftrightarrow & -225x+60x& = & 40+36 \\\Leftrightarrow & \color{red}{-165} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-165} & & \\\Leftrightarrow & x = \frac{-76}{165} & & \\ & V = \left\{ \frac{-76}{165} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-198} & = & \color{red}{275x} +40 \\\Leftrightarrow & -1320x \color{red}{-198} \color{blue}{+198} \color{blue}{-275x} & = & \color{red}{275x} +40 \color{blue}{-275x} \color{blue}{+198} \\\Leftrightarrow & -1320x-275x& = & 40+198 \\\Leftrightarrow & \color{red}{-1595} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-1595} & & \\\Leftrightarrow & x = \frac{-238}{1595} & & \\ & V = \left\{ \frac{-238}{1595} \right\} & \\\end{align}\)
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