Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{3})& = & 9x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 9x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+8} & = & \color{red}{27x} +8 \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & 24x-27x& = & 8-8 \\\Leftrightarrow & \color{red}{-3} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-3} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-210x} +35 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-36} \\\Leftrightarrow & 180x+210x& = & 35-36 \\\Leftrightarrow & \color{red}{390} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{390} & & \\ & V = \left\{ \frac{-1}{390} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{4}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+168} & = & \color{red}{245x} +40 \\\Leftrightarrow & 630x \color{red}{+168} \color{blue}{-168} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{-168} \\\Leftrightarrow & 630x-245x& = & 40-168 \\\Leftrightarrow & \color{red}{385} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{385} & & \\ & V = \left\{ \frac{-128}{385} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{11})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{30}{11}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+150} & = & \color{red}{275x} +66 \\\Leftrightarrow & -660x \color{red}{+150} \color{blue}{-150} \color{blue}{-275x} & = & \color{red}{275x} +66 \color{blue}{-275x} \color{blue}{-150} \\\Leftrightarrow & -660x-275x& = & 66-150 \\\Leftrightarrow & \color{red}{-935} x& = & -84 \\\Leftrightarrow & x = \frac{-84}{-935} & & \\\Leftrightarrow & x = \frac{84}{935} & & \\ & V = \left\{ \frac{84}{935} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{5}{8})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 6x+\frac{15}{8}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{528}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{440}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 528x \color{red}{+165} & = & \color{red}{440x} +48 \\\Leftrightarrow & 528x \color{red}{+165} \color{blue}{-165} \color{blue}{-440x} & = & \color{red}{440x} +48 \color{blue}{-440x} \color{blue}{-165} \\\Leftrightarrow & 528x-440x& = & 48-165 \\\Leftrightarrow & \color{red}{88} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{88} & & \\ & V = \left\{ \frac{-117}{88} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{-18} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -126x \color{red}{-18} \color{blue}{+18} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{+18} \\\Leftrightarrow & -126x+147x& = & 70+18 \\\Leftrightarrow & \color{red}{21} x& = & 88 \\\Leftrightarrow & x = \frac{88}{21} & & \\ & V = \left\{ \frac{88}{21} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{9})& = & -7x+\frac{7}{11} \\\Leftrightarrow & 10x+\frac{8}{9}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{63}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+88} & = & \color{red}{-693x} +63 \\\Leftrightarrow & 990x \color{red}{+88} \color{blue}{-88} \color{blue}{+693x} & = & \color{red}{-693x} +63 \color{blue}{+693x} \color{blue}{-88} \\\Leftrightarrow & 990x+693x& = & 63-88 \\\Leftrightarrow & \color{red}{1683} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1683} & & \\ & V = \left\{ \frac{-25}{1683} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{2}{5})& = & -8x+\frac{5}{6} \\\Leftrightarrow & -21x+\frac{14}{5}& = & -8x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-630}{ \color{blue}{30} }x+ \frac{84}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -630x \color{red}{+84} & = & \color{red}{-240x} +25 \\\Leftrightarrow & -630x \color{red}{+84} \color{blue}{-84} \color{blue}{+240x} & = & \color{red}{-240x} +25 \color{blue}{+240x} \color{blue}{-84} \\\Leftrightarrow & -630x+240x& = & 25-84 \\\Leftrightarrow & \color{red}{-390} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{-390} & & \\\Leftrightarrow & x = \frac{59}{390} & & \\ & V = \left\{ \frac{59}{390} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{8})& = & 9x+\frac{4}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{216}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{216x} +32 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{-216x} & = & \color{red}{216x} +32 \color{blue}{-216x} \color{blue}{-63} \\\Leftrightarrow & -672x-216x& = & 32-63 \\\Leftrightarrow & \color{red}{-888} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-888} & & \\\Leftrightarrow & x = \frac{31}{888} & & \\ & V = \left\{ \frac{31}{888} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{-126} & = & \color{red}{539x} +110 \\\Leftrightarrow & -2310x \color{red}{-126} \color{blue}{+126} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+126} \\\Leftrightarrow & -2310x-539x& = & 110+126 \\\Leftrightarrow & \color{red}{-2849} x& = & 236 \\\Leftrightarrow & x = \frac{236}{-2849} & & \\\Leftrightarrow & x = \frac{-236}{2849} & & \\ & V = \left\{ \frac{-236}{2849} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{2})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 25x-\frac{25}{2}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{200}{ \color{blue}{8} }x- \frac{100}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 200x \color{red}{-100} & = & \color{red}{24x} +7 \\\Leftrightarrow & 200x \color{red}{-100} \color{blue}{+100} \color{blue}{-24x} & = & \color{red}{24x} +7 \color{blue}{-24x} \color{blue}{+100} \\\Leftrightarrow & 200x-24x& = & 7+100 \\\Leftrightarrow & \color{red}{176} x& = & 107 \\\Leftrightarrow & x = \frac{107}{176} & & \\ & V = \left\{ \frac{107}{176} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & 15x-\frac{25}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{25}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-25} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 45x \color{red}{-25} \color{blue}{+25} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+25} \\\Leftrightarrow & 45x+21x& = & 10+25 \\\Leftrightarrow & \color{red}{66} x& = & 35 \\\Leftrightarrow & x = \frac{35}{66} & & \\ & V = \left\{ \frac{35}{66} \right\} & \\\end{align}\)
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