Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 20x+\frac{25}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{25}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+25} & = & \color{red}{9x} +8 \\\Leftrightarrow & 60x \color{red}{+25} \color{blue}{-25} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{-25} \\\Leftrightarrow & 60x-9x& = & 8-25 \\\Leftrightarrow & \color{red}{51} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{51} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{3})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -16x+\frac{8}{3}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x+ \frac{80}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{+80} & = & \color{red}{210x} +27 \\\Leftrightarrow & -480x \color{red}{+80} \color{blue}{-80} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{-80} \\\Leftrightarrow & -480x-210x& = & 27-80 \\\Leftrightarrow & \color{red}{-690} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-690} & & \\\Leftrightarrow & x = \frac{53}{690} & & \\ & V = \left\{ \frac{53}{690} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-60}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{-48} & = & \color{red}{-60x} +15 \\\Leftrightarrow & 400x \color{red}{-48} \color{blue}{+48} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{+48} \\\Leftrightarrow & 400x+60x& = & 15+48 \\\Leftrightarrow & \color{red}{460} x& = & 63 \\\Leftrightarrow & x = \frac{63}{460} & & \\ & V = \left\{ \frac{63}{460} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{16}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{144}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+144} & = & \color{red}{441x} +70 \\\Leftrightarrow & 756x \color{red}{+144} \color{blue}{-144} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-144} \\\Leftrightarrow & 756x-441x& = & 70-144 \\\Leftrightarrow & \color{red}{315} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{315} & & \\ & V = \left\{ \frac{-74}{315} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{3})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -4x-\frac{10}{3}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-70} & = & \color{red}{105x} +30 \\\Leftrightarrow & -84x \color{red}{-70} \color{blue}{+70} \color{blue}{-105x} & = & \color{red}{105x} +30 \color{blue}{-105x} \color{blue}{+70} \\\Leftrightarrow & -84x-105x& = & 30+70 \\\Leftrightarrow & \color{red}{-189} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-189} & & \\\Leftrightarrow & x = \frac{-100}{189} & & \\ & V = \left\{ \frac{-100}{189} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{20}{3}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{-20} & = & \color{red}{-15x} +8 \\\Leftrightarrow & 24x \color{red}{-20} \color{blue}{+20} \color{blue}{+15x} & = & \color{red}{-15x} +8 \color{blue}{+15x} \color{blue}{+20} \\\Leftrightarrow & 24x+15x& = & 8+20 \\\Leftrightarrow & \color{red}{39} x& = & 28 \\\Leftrightarrow & x = \frac{28}{39} & & \\ & V = \left\{ \frac{28}{39} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 35x-\frac{21}{8}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{1400}{ \color{blue}{40} }x- \frac{105}{ \color{blue}{40} })& = & (\frac{-320}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 1400x \color{red}{-105} & = & \color{red}{-320x} +48 \\\Leftrightarrow & 1400x \color{red}{-105} \color{blue}{+105} \color{blue}{+320x} & = & \color{red}{-320x} +48 \color{blue}{+320x} \color{blue}{+105} \\\Leftrightarrow & 1400x+320x& = & 48+105 \\\Leftrightarrow & \color{red}{1720} x& = & 153 \\\Leftrightarrow & x = \frac{153}{1720} & & \\ & V = \left\{ \frac{153}{1720} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x-\frac{12}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{-108} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -2970x \color{red}{-108} \color{blue}{+108} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{+108} \\\Leftrightarrow & -2970x+693x& = & 22+108 \\\Leftrightarrow & \color{red}{-2277} x& = & 130 \\\Leftrightarrow & x = \frac{130}{-2277} & & \\\Leftrightarrow & x = \frac{-130}{2277} & & \\ & V = \left\{ \frac{-130}{2277} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-150} & = & \color{red}{175x} +42 \\\Leftrightarrow & 420x \color{red}{-150} \color{blue}{+150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+150} \\\Leftrightarrow & 420x-175x& = & 42+150 \\\Leftrightarrow & \color{red}{245} x& = & 192 \\\Leftrightarrow & x = \frac{192}{245} & & \\ & V = \left\{ \frac{192}{245} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x-\frac{15}{8}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{-15} & = & \color{red}{-56x} +12 \\\Leftrightarrow & -80x \color{red}{-15} \color{blue}{+15} \color{blue}{+56x} & = & \color{red}{-56x} +12 \color{blue}{+56x} \color{blue}{+15} \\\Leftrightarrow & -80x+56x& = & 12+15 \\\Leftrightarrow & \color{red}{-24} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-24} & & \\\Leftrightarrow & x = \frac{-9}{8} & & \\ & V = \left\{ \frac{-9}{8} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+162} & = & \color{red}{-693x} +22 \\\Leftrightarrow & -2970x \color{red}{+162} \color{blue}{-162} \color{blue}{+693x} & = & \color{red}{-693x} +22 \color{blue}{+693x} \color{blue}{-162} \\\Leftrightarrow & -2970x+693x& = & 22-162 \\\Leftrightarrow & \color{red}{-2277} x& = & -140 \\\Leftrightarrow & x = \frac{-140}{-2277} & & \\\Leftrightarrow & x = \frac{140}{2277} & & \\ & V = \left\{ \frac{140}{2277} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{3})& = & 8x+\frac{3}{5} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+70} & = & \color{red}{120x} +9 \\\Leftrightarrow & -315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +9 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & -315x-120x& = & 9-70 \\\Leftrightarrow & \color{red}{-435} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-435} & & \\\Leftrightarrow & x = \frac{61}{435} & & \\ & V = \left\{ \frac{61}{435} \right\} & \\\end{align}\)
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