Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{3}{4})& = & 4x+\frac{7}{5} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 4x+\frac{7}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-300}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{28}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -300x \color{red}{+75} & = & \color{red}{80x} +28 \\\Leftrightarrow & -300x \color{red}{+75} \color{blue}{-75} \color{blue}{-80x} & = & \color{red}{80x} +28 \color{blue}{-80x} \color{blue}{-75} \\\Leftrightarrow & -300x-80x& = & 28-75 \\\Leftrightarrow & \color{red}{-380} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-380} & & \\\Leftrightarrow & x = \frac{47}{380} & & \\ & V = \left\{ \frac{47}{380} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{4}{11})& = & 5x+\frac{9}{4} \\\Leftrightarrow & 12x+\frac{24}{11}& = & 5x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{528}{ \color{blue}{44} }x+ \frac{96}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 528x \color{red}{+96} & = & \color{red}{220x} +99 \\\Leftrightarrow & 528x \color{red}{+96} \color{blue}{-96} \color{blue}{-220x} & = & \color{red}{220x} +99 \color{blue}{-220x} \color{blue}{-96} \\\Leftrightarrow & 528x-220x& = & 99-96 \\\Leftrightarrow & \color{red}{308} x& = & 3 \\\Leftrightarrow & x = \frac{3}{308} & & \\ & V = \left\{ \frac{3}{308} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{5}{11})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -14x+\frac{35}{11}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x+ \frac{175}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{+175} & = & \color{red}{-275x} +22 \\\Leftrightarrow & -770x \color{red}{+175} \color{blue}{-175} \color{blue}{+275x} & = & \color{red}{-275x} +22 \color{blue}{+275x} \color{blue}{-175} \\\Leftrightarrow & -770x+275x& = & 22-175 \\\Leftrightarrow & \color{red}{-495} x& = & -153 \\\Leftrightarrow & x = \frac{-153}{-495} & & \\\Leftrightarrow & x = \frac{17}{55} & & \\ & V = \left\{ \frac{17}{55} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{5}{2})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 10x-\frac{25}{2}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{220}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 220x \color{red}{-275} & = & \color{red}{66x} +8 \\\Leftrightarrow & 220x \color{red}{-275} \color{blue}{+275} \color{blue}{-66x} & = & \color{red}{66x} +8 \color{blue}{-66x} \color{blue}{+275} \\\Leftrightarrow & 220x-66x& = & 8+275 \\\Leftrightarrow & \color{red}{154} x& = & 283 \\\Leftrightarrow & x = \frac{283}{154} & & \\ & V = \left\{ \frac{283}{154} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+100} & = & \color{red}{-105x} +12 \\\Leftrightarrow & -300x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +12 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -300x+105x& = & 12-100 \\\Leftrightarrow & \color{red}{-195} x& = & -88 \\\Leftrightarrow & x = \frac{-88}{-195} & & \\\Leftrightarrow & x = \frac{88}{195} & & \\ & V = \left\{ \frac{88}{195} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & -8x+\frac{9}{10} \\\Leftrightarrow & -21x+\frac{35}{9}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1890}{ \color{blue}{90} }x+ \frac{350}{ \color{blue}{90} })& = & (\frac{-720}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1890x \color{red}{+350} & = & \color{red}{-720x} +81 \\\Leftrightarrow & -1890x \color{red}{+350} \color{blue}{-350} \color{blue}{+720x} & = & \color{red}{-720x} +81 \color{blue}{+720x} \color{blue}{-350} \\\Leftrightarrow & -1890x+720x& = & 81-350 \\\Leftrightarrow & \color{red}{-1170} x& = & -269 \\\Leftrightarrow & x = \frac{-269}{-1170} & & \\\Leftrightarrow & x = \frac{269}{1170} & & \\ & V = \left\{ \frac{269}{1170} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-126} & = & \color{red}{385x} +33 \\\Leftrightarrow & -1848x \color{red}{-126} \color{blue}{+126} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{+126} \\\Leftrightarrow & -1848x-385x& = & 33+126 \\\Leftrightarrow & \color{red}{-2233} x& = & 159 \\\Leftrightarrow & x = \frac{159}{-2233} & & \\\Leftrightarrow & x = \frac{-159}{2233} & & \\ & V = \left\{ \frac{-159}{2233} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -24x-\frac{18}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{110x} +33 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{+36} \\\Leftrightarrow & -528x-110x& = & 33+36 \\\Leftrightarrow & \color{red}{-638} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-638} & & \\\Leftrightarrow & x = \frac{-69}{638} & & \\ & V = \left\{ \frac{-69}{638} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{9})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -16x-\frac{20}{9}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{220}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-220} & = & \color{red}{693x} +45 \\\Leftrightarrow & -1584x \color{red}{-220} \color{blue}{+220} \color{blue}{-693x} & = & \color{red}{693x} +45 \color{blue}{-693x} \color{blue}{+220} \\\Leftrightarrow & -1584x-693x& = & 45+220 \\\Leftrightarrow & \color{red}{-2277} x& = & 265 \\\Leftrightarrow & x = \frac{265}{-2277} & & \\\Leftrightarrow & x = \frac{-265}{2277} & & \\ & V = \left\{ \frac{-265}{2277} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{105x} +10 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{+28} \\\Leftrightarrow & 140x-105x& = & 10+28 \\\Leftrightarrow & \color{red}{35} x& = & 38 \\\Leftrightarrow & x = \frac{38}{35} & & \\ & V = \left\{ \frac{38}{35} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x+\frac{24}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+24} & = & \color{red}{77x} +6 \\\Leftrightarrow & -330x \color{red}{+24} \color{blue}{-24} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-24} \\\Leftrightarrow & -330x-77x& = & 6-24 \\\Leftrightarrow & \color{red}{-407} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-407} & & \\\Leftrightarrow & x = \frac{18}{407} & & \\ & V = \left\{ \frac{18}{407} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{105x} +40 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +40 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -300x-105x& = & 40+36 \\\Leftrightarrow & \color{red}{-405} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-405} & & \\\Leftrightarrow & x = \frac{-76}{405} & & \\ & V = \left\{ \frac{-76}{405} \right\} & \\\end{align}\)
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