Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{12}{5}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+36} & = & \color{red}{105x} +20 \\\Leftrightarrow & -90x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & -90x-105x& = & 20-36 \\\Leftrightarrow & \color{red}{-195} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-195} & & \\\Leftrightarrow & x = \frac{16}{195} & & \\ & V = \left\{ \frac{16}{195} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{4}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 10x-\frac{8}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-40} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 550x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & 550x+385x& = & 66+40 \\\Leftrightarrow & \color{red}{935} x& = & 106 \\\Leftrightarrow & x = \frac{106}{935} & & \\ & V = \left\{ \frac{106}{935} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{2}{5})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 14x+\frac{14}{5}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{490}{ \color{blue}{35} }x+ \frac{98}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 490x \color{red}{+98} & = & \color{red}{-175x} +30 \\\Leftrightarrow & 490x \color{red}{+98} \color{blue}{-98} \color{blue}{+175x} & = & \color{red}{-175x} +30 \color{blue}{+175x} \color{blue}{-98} \\\Leftrightarrow & 490x+175x& = & 30-98 \\\Leftrightarrow & \color{red}{665} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{665} & & \\ & V = \left\{ \frac{-68}{665} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -6x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -6x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{154}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+154} & = & \color{red}{-198x} +18 \\\Leftrightarrow & -1155x \color{red}{+154} \color{blue}{-154} \color{blue}{+198x} & = & \color{red}{-198x} +18 \color{blue}{+198x} \color{blue}{-154} \\\Leftrightarrow & -1155x+198x& = & 18-154 \\\Leftrightarrow & \color{red}{-957} x& = & -136 \\\Leftrightarrow & x = \frac{-136}{-957} & & \\\Leftrightarrow & x = \frac{136}{957} & & \\ & V = \left\{ \frac{136}{957} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{11})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{16}{11}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-112} & = & \color{red}{385x} +88 \\\Leftrightarrow & 924x \color{red}{-112} \color{blue}{+112} \color{blue}{-385x} & = & \color{red}{385x} +88 \color{blue}{-385x} \color{blue}{+112} \\\Leftrightarrow & 924x-385x& = & 88+112 \\\Leftrightarrow & \color{red}{539} x& = & 200 \\\Leftrightarrow & x = \frac{200}{539} & & \\ & V = \left\{ \frac{200}{539} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{4})& = & 3x+\frac{8}{9} \\\Leftrightarrow & -20x+\frac{15}{4}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{+135} & = & \color{red}{108x} +32 \\\Leftrightarrow & -720x \color{red}{+135} \color{blue}{-135} \color{blue}{-108x} & = & \color{red}{108x} +32 \color{blue}{-108x} \color{blue}{-135} \\\Leftrightarrow & -720x-108x& = & 32-135 \\\Leftrightarrow & \color{red}{-828} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{-828} & & \\\Leftrightarrow & x = \frac{103}{828} & & \\ & V = \left\{ \frac{103}{828} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{30}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{+330} & = & \color{red}{385x} +42 \\\Leftrightarrow & -1386x \color{red}{+330} \color{blue}{-330} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{-330} \\\Leftrightarrow & -1386x-385x& = & 42-330 \\\Leftrightarrow & \color{red}{-1771} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{-1771} & & \\\Leftrightarrow & x = \frac{288}{1771} & & \\ & V = \left\{ \frac{288}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{7})& = & -9x+\frac{2}{3} \\\Leftrightarrow & 10x+\frac{20}{7}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{+60} & = & \color{red}{-189x} +14 \\\Leftrightarrow & 210x \color{red}{+60} \color{blue}{-60} \color{blue}{+189x} & = & \color{red}{-189x} +14 \color{blue}{+189x} \color{blue}{-60} \\\Leftrightarrow & 210x+189x& = & 14-60 \\\Leftrightarrow & \color{red}{399} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{399} & & \\ & V = \left\{ \frac{-46}{399} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & 3x+\frac{10}{9} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+90} & = & \color{red}{189x} +70 \\\Leftrightarrow & -504x \color{red}{+90} \color{blue}{-90} \color{blue}{-189x} & = & \color{red}{189x} +70 \color{blue}{-189x} \color{blue}{-90} \\\Leftrightarrow & -504x-189x& = & 70-90 \\\Leftrightarrow & \color{red}{-693} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-693} & & \\\Leftrightarrow & x = \frac{20}{693} & & \\ & V = \left\{ \frac{20}{693} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{4}{11})& = & -8x+\frac{9}{7} \\\Leftrightarrow & -15x+\frac{20}{11}& = & -8x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+140} & = & \color{red}{-616x} +99 \\\Leftrightarrow & -1155x \color{red}{+140} \color{blue}{-140} \color{blue}{+616x} & = & \color{red}{-616x} +99 \color{blue}{+616x} \color{blue}{-140} \\\Leftrightarrow & -1155x+616x& = & 99-140 \\\Leftrightarrow & \color{red}{-539} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-539} & & \\\Leftrightarrow & x = \frac{41}{539} & & \\ & V = \left\{ \frac{41}{539} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{11})& = & -7x+\frac{4}{5} \\\Leftrightarrow & 10x-\frac{6}{11}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-30} & = & \color{red}{-385x} +44 \\\Leftrightarrow & 550x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +44 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & 550x+385x& = & 44+30 \\\Leftrightarrow & \color{red}{935} x& = & 74 \\\Leftrightarrow & x = \frac{74}{935} & & \\ & V = \left\{ \frac{74}{935} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{11})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -15x+\frac{6}{11}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{+18} & = & \color{red}{132x} +88 \\\Leftrightarrow & -495x \color{red}{+18} \color{blue}{-18} \color{blue}{-132x} & = & \color{red}{132x} +88 \color{blue}{-132x} \color{blue}{-18} \\\Leftrightarrow & -495x-132x& = & 88-18 \\\Leftrightarrow & \color{red}{-627} x& = & 70 \\\Leftrightarrow & x = \frac{70}{-627} & & \\\Leftrightarrow & x = \frac{-70}{627} & & \\ & V = \left\{ \frac{-70}{627} \right\} & \\\end{align}\)
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