Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{15}{8}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{56x} +6 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{-56x} & = & \color{red}{56x} +6 \color{blue}{-56x} \color{blue}{-15} \\\Leftrightarrow & -80x-56x& = & 6-15 \\\Leftrightarrow & \color{red}{-136} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-136} & & \\\Leftrightarrow & x = \frac{9}{136} & & \\ & V = \left\{ \frac{9}{136} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{2}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -16x-\frac{8}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-24} & = & \color{red}{231x} +44 \\\Leftrightarrow & -528x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -528x-231x& = & 44+24 \\\Leftrightarrow & \color{red}{-759} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-759} & & \\\Leftrightarrow & x = \frac{-68}{759} & & \\ & V = \left\{ \frac{-68}{759} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x-\frac{6}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-198}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -198x \color{red}{-18} & = & \color{red}{231x} +88 \\\Leftrightarrow & -198x \color{red}{-18} \color{blue}{+18} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{+18} \\\Leftrightarrow & -198x-231x& = & 88+18 \\\Leftrightarrow & \color{red}{-429} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-429} & & \\\Leftrightarrow & x = \frac{-106}{429} & & \\ & V = \left\{ \frac{-106}{429} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{6}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-18} & = & \color{red}{-75x} +50 \\\Leftrightarrow & -180x \color{red}{-18} \color{blue}{+18} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+18} \\\Leftrightarrow & -180x+75x& = & 50+18 \\\Leftrightarrow & \color{red}{-105} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-105} & & \\\Leftrightarrow & x = \frac{-68}{105} & & \\ & V = \left\{ \frac{-68}{105} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{5}{7})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x- \frac{30}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{-30} & = & \color{red}{35x} +5 \\\Leftrightarrow & -168x \color{red}{-30} \color{blue}{+30} \color{blue}{-35x} & = & \color{red}{35x} +5 \color{blue}{-35x} \color{blue}{+30} \\\Leftrightarrow & -168x-35x& = & 5+30 \\\Leftrightarrow & \color{red}{-203} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-203} & & \\\Leftrightarrow & x = \frac{-5}{29} & & \\ & V = \left\{ \frac{-5}{29} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -28x+\frac{21}{11}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{+21} & = & \color{red}{33x} +3 \\\Leftrightarrow & -308x \color{red}{+21} \color{blue}{-21} \color{blue}{-33x} & = & \color{red}{33x} +3 \color{blue}{-33x} \color{blue}{-21} \\\Leftrightarrow & -308x-33x& = & 3-21 \\\Leftrightarrow & \color{red}{-341} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{-341} & & \\\Leftrightarrow & x = \frac{18}{341} & & \\ & V = \left\{ \frac{18}{341} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x- \frac{70}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{-70} & = & \color{red}{54x} +81 \\\Leftrightarrow & -630x \color{red}{-70} \color{blue}{+70} \color{blue}{-54x} & = & \color{red}{54x} +81 \color{blue}{-54x} \color{blue}{+70} \\\Leftrightarrow & -630x-54x& = & 81+70 \\\Leftrightarrow & \color{red}{-684} x& = & 151 \\\Leftrightarrow & x = \frac{151}{-684} & & \\\Leftrightarrow & x = \frac{-151}{684} & & \\ & V = \left\{ \frac{-151}{684} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{3})& = & 9x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 9x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+60} & = & \color{red}{81x} +2 \\\Leftrightarrow & 180x \color{red}{+60} \color{blue}{-60} \color{blue}{-81x} & = & \color{red}{81x} +2 \color{blue}{-81x} \color{blue}{-60} \\\Leftrightarrow & 180x-81x& = & 2-60 \\\Leftrightarrow & \color{red}{99} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{99} & & \\ & V = \left\{ \frac{-58}{99} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & 770x+539x& = & 42+110 \\\Leftrightarrow & \color{red}{1309} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1309} & & \\ & V = \left\{ \frac{152}{1309} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & 3x+\frac{3}{11} \\\Leftrightarrow & -20x-\frac{15}{4}& = & 3x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-880}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{132}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -880x \color{red}{-165} & = & \color{red}{132x} +12 \\\Leftrightarrow & -880x \color{red}{-165} \color{blue}{+165} \color{blue}{-132x} & = & \color{red}{132x} +12 \color{blue}{-132x} \color{blue}{+165} \\\Leftrightarrow & -880x-132x& = & 12+165 \\\Leftrightarrow & \color{red}{-1012} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-1012} & & \\\Leftrightarrow & x = \frac{-177}{1012} & & \\ & V = \left\{ \frac{-177}{1012} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{11})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -6x-\frac{4}{11}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{28}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-28} & = & \color{red}{-539x} +66 \\\Leftrightarrow & -462x \color{red}{-28} \color{blue}{+28} \color{blue}{+539x} & = & \color{red}{-539x} +66 \color{blue}{+539x} \color{blue}{+28} \\\Leftrightarrow & -462x+539x& = & 66+28 \\\Leftrightarrow & \color{red}{77} x& = & 94 \\\Leftrightarrow & x = \frac{94}{77} & & \\ & V = \left\{ \frac{94}{77} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{4}{5} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-30} & = & \color{red}{-245x} +28 \\\Leftrightarrow & -210x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +28 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & -210x+245x& = & 28+30 \\\Leftrightarrow & \color{red}{35} x& = & 58 \\\Leftrightarrow & x = \frac{58}{35} & & \\ & V = \left\{ \frac{58}{35} \right\} & \\\end{align}\)
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