Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-480}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-168}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -480x \color{red}{+45} & = & \color{red}{-168x} +80 \\\Leftrightarrow & -480x \color{red}{+45} \color{blue}{-45} \color{blue}{+168x} & = & \color{red}{-168x} +80 \color{blue}{+168x} \color{blue}{-45} \\\Leftrightarrow & -480x+168x& = & 80-45 \\\Leftrightarrow & \color{red}{-312} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-312} & & \\\Leftrightarrow & x = \frac{-35}{312} & & \\ & V = \left\{ \frac{-35}{312} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{3})& = & 5x+\frac{5}{8} \\\Leftrightarrow & -4x+\frac{4}{3}& = & 5x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -96x \color{red}{+32} & = & \color{red}{120x} +15 \\\Leftrightarrow & -96x \color{red}{+32} \color{blue}{-32} \color{blue}{-120x} & = & \color{red}{120x} +15 \color{blue}{-120x} \color{blue}{-32} \\\Leftrightarrow & -96x-120x& = & 15-32 \\\Leftrightarrow & \color{red}{-216} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-216} & & \\\Leftrightarrow & x = \frac{17}{216} & & \\ & V = \left\{ \frac{17}{216} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{7})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x+4& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x+ \frac{12}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{+12} & = & \color{red}{24x} +2 \\\Leftrightarrow & -63x \color{red}{+12} \color{blue}{-12} \color{blue}{-24x} & = & \color{red}{24x} +2 \color{blue}{-24x} \color{blue}{-12} \\\Leftrightarrow & -63x-24x& = & 2-12 \\\Leftrightarrow & \color{red}{-87} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-87} & & \\\Leftrightarrow & x = \frac{10}{87} & & \\ & V = \left\{ \frac{10}{87} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{5})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -30x+\frac{18}{5}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{126}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+126} & = & \color{red}{245x} +30 \\\Leftrightarrow & -1050x \color{red}{+126} \color{blue}{-126} \color{blue}{-245x} & = & \color{red}{245x} +30 \color{blue}{-245x} \color{blue}{-126} \\\Leftrightarrow & -1050x-245x& = & 30-126 \\\Leftrightarrow & \color{red}{-1295} x& = & -96 \\\Leftrightarrow & x = \frac{-96}{-1295} & & \\\Leftrightarrow & x = \frac{96}{1295} & & \\ & V = \left\{ \frac{96}{1295} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{75}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-75} & = & \color{red}{385x} +66 \\\Leftrightarrow & -550x \color{red}{-75} \color{blue}{+75} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+75} \\\Leftrightarrow & -550x-385x& = & 66+75 \\\Leftrightarrow & \color{red}{-935} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-935} & & \\\Leftrightarrow & x = \frac{-141}{935} & & \\ & V = \left\{ \frac{-141}{935} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{11})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -6x+\frac{15}{11}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+15} & = & \color{red}{77x} +10 \\\Leftrightarrow & -66x \color{red}{+15} \color{blue}{-15} \color{blue}{-77x} & = & \color{red}{77x} +10 \color{blue}{-77x} \color{blue}{-15} \\\Leftrightarrow & -66x-77x& = & 10-15 \\\Leftrightarrow & \color{red}{-143} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-143} & & \\\Leftrightarrow & x = \frac{5}{143} & & \\ & V = \left\{ \frac{5}{143} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{2}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{8}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-24} & = & \color{red}{165x} +88 \\\Leftrightarrow & -396x \color{red}{-24} \color{blue}{+24} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+24} \\\Leftrightarrow & -396x-165x& = & 88+24 \\\Leftrightarrow & \color{red}{-561} x& = & 112 \\\Leftrightarrow & x = \frac{112}{-561} & & \\\Leftrightarrow & x = \frac{-112}{561} & & \\ & V = \left\{ \frac{-112}{561} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-162}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-162x} +21 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+162x} & = & \color{red}{-162x} +21 \color{blue}{+162x} \color{blue}{+16} \\\Leftrightarrow & -72x+162x& = & 21+16 \\\Leftrightarrow & \color{red}{90} x& = & 37 \\\Leftrightarrow & x = \frac{37}{90} & & \\ & V = \left\{ \frac{37}{90} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+56} & = & \color{red}{-441x} +36 \\\Leftrightarrow & -1008x \color{red}{+56} \color{blue}{-56} \color{blue}{+441x} & = & \color{red}{-441x} +36 \color{blue}{+441x} \color{blue}{-56} \\\Leftrightarrow & -1008x+441x& = & 36-56 \\\Leftrightarrow & \color{red}{-567} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{-567} & & \\\Leftrightarrow & x = \frac{20}{567} & & \\ & V = \left\{ \frac{20}{567} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -20x-\frac{10}{3}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-10} & = & \color{red}{-21x} +2 \\\Leftrightarrow & -60x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +2 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & -60x+21x& = & 2+10 \\\Leftrightarrow & \color{red}{-39} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-39} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{3}{4})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{-196}{ \color{blue}{28} }x+ \frac{8}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{+105} & = & \color{red}{-196x} +8 \\\Leftrightarrow & 420x \color{red}{+105} \color{blue}{-105} \color{blue}{+196x} & = & \color{red}{-196x} +8 \color{blue}{+196x} \color{blue}{-105} \\\Leftrightarrow & 420x+196x& = & 8-105 \\\Leftrightarrow & \color{red}{616} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{616} & & \\ & V = \left\{ \frac{-97}{616} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{7})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -25x+\frac{20}{7}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-875}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -875x \color{red}{+100} & = & \color{red}{315x} +63 \\\Leftrightarrow & -875x \color{red}{+100} \color{blue}{-100} \color{blue}{-315x} & = & \color{red}{315x} +63 \color{blue}{-315x} \color{blue}{-100} \\\Leftrightarrow & -875x-315x& = & 63-100 \\\Leftrightarrow & \color{red}{-1190} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-1190} & & \\\Leftrightarrow & x = \frac{37}{1190} & & \\ & V = \left\{ \frac{37}{1190} \right\} & \\\end{align}\)
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