Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{7})& = & 6x+\frac{5}{11} \\\Leftrightarrow & -25x+\frac{15}{7}& = & 6x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{165}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+165} & = & \color{red}{462x} +35 \\\Leftrightarrow & -1925x \color{red}{+165} \color{blue}{-165} \color{blue}{-462x} & = & \color{red}{462x} +35 \color{blue}{-462x} \color{blue}{-165} \\\Leftrightarrow & -1925x-462x& = & 35-165 \\\Leftrightarrow & \color{red}{-2387} x& = & -130 \\\Leftrightarrow & x = \frac{-130}{-2387} & & \\\Leftrightarrow & x = \frac{130}{2387} & & \\ & V = \left\{ \frac{130}{2387} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{8}{9}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1260x \color{red}{-56} & = & \color{red}{441x} +54 \\\Leftrightarrow & 1260x \color{red}{-56} \color{blue}{+56} \color{blue}{-441x} & = & \color{red}{441x} +54 \color{blue}{-441x} \color{blue}{+56} \\\Leftrightarrow & 1260x-441x& = & 54+56 \\\Leftrightarrow & \color{red}{819} x& = & 110 \\\Leftrightarrow & x = \frac{110}{819} & & \\ & V = \left\{ \frac{110}{819} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 7x+\frac{3}{7} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+56} & = & \color{red}{147x} +9 \\\Leftrightarrow & 252x \color{red}{+56} \color{blue}{-56} \color{blue}{-147x} & = & \color{red}{147x} +9 \color{blue}{-147x} \color{blue}{-56} \\\Leftrightarrow & 252x-147x& = & 9-56 \\\Leftrightarrow & \color{red}{105} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{105} & & \\ & V = \left\{ \frac{-47}{105} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{9})& = & -9x+\frac{9}{7} \\\Leftrightarrow & 4x-\frac{10}{9}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x- \frac{70}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{-70} & = & \color{red}{-567x} +81 \\\Leftrightarrow & 252x \color{red}{-70} \color{blue}{+70} \color{blue}{+567x} & = & \color{red}{-567x} +81 \color{blue}{+567x} \color{blue}{+70} \\\Leftrightarrow & 252x+567x& = & 81+70 \\\Leftrightarrow & \color{red}{819} x& = & 151 \\\Leftrightarrow & x = \frac{151}{819} & & \\ & V = \left\{ \frac{151}{819} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{5}{11})& = & 9x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{20}{11}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{180}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-180} & = & \color{red}{891x} +110 \\\Leftrightarrow & -792x \color{red}{-180} \color{blue}{+180} \color{blue}{-891x} & = & \color{red}{891x} +110 \color{blue}{-891x} \color{blue}{+180} \\\Leftrightarrow & -792x-891x& = & 110+180 \\\Leftrightarrow & \color{red}{-1683} x& = & 290 \\\Leftrightarrow & x = \frac{290}{-1683} & & \\\Leftrightarrow & x = \frac{-290}{1683} & & \\ & V = \left\{ \frac{-290}{1683} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{-12} & = & \color{red}{-15x} +6 \\\Leftrightarrow & -40x \color{red}{-12} \color{blue}{+12} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{+12} \\\Leftrightarrow & -40x+15x& = & 6+12 \\\Leftrightarrow & \color{red}{-25} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-25} & & \\\Leftrightarrow & x = \frac{-18}{25} & & \\ & V = \left\{ \frac{-18}{25} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -9x+\frac{3}{2} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-252}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-60} \\\Leftrightarrow & -252x+126x& = & 21-60 \\\Leftrightarrow & \color{red}{-126} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-126} & & \\\Leftrightarrow & x = \frac{13}{42} & & \\ & V = \left\{ \frac{13}{42} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 6x+\frac{6}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{330}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 330x \color{red}{+66} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 330x \color{red}{+66} \color{blue}{-66} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{-66} \\\Leftrightarrow & 330x+385x& = & 10-66 \\\Leftrightarrow & \color{red}{715} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{715} & & \\ & V = \left\{ \frac{-56}{715} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{9})& = & 3x+\frac{5}{12} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-504}{ \color{blue}{36} }x- \frac{140}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{15}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -504x \color{red}{-140} & = & \color{red}{108x} +15 \\\Leftrightarrow & -504x \color{red}{-140} \color{blue}{+140} \color{blue}{-108x} & = & \color{red}{108x} +15 \color{blue}{-108x} \color{blue}{+140} \\\Leftrightarrow & -504x-108x& = & 15+140 \\\Leftrightarrow & \color{red}{-612} x& = & 155 \\\Leftrightarrow & x = \frac{155}{-612} & & \\\Leftrightarrow & x = \frac{-155}{612} & & \\ & V = \left\{ \frac{-155}{612} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{3})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -14x-\frac{14}{3}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -294x \color{red}{-98} & = & \color{red}{-105x} +15 \\\Leftrightarrow & -294x \color{red}{-98} \color{blue}{+98} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{+98} \\\Leftrightarrow & -294x+105x& = & 15+98 \\\Leftrightarrow & \color{red}{-189} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-189} & & \\\Leftrightarrow & x = \frac{-113}{189} & & \\ & V = \left\{ \frac{-113}{189} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{-175x} +10 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +10 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -420x+175x& = & 10+84 \\\Leftrightarrow & \color{red}{-245} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-245} & & \\\Leftrightarrow & x = \frac{-94}{245} & & \\ & V = \left\{ \frac{-94}{245} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{3}{4} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1056}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1056x \color{red}{+72} & = & \color{red}{220x} +33 \\\Leftrightarrow & 1056x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +33 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & 1056x-220x& = & 33-72 \\\Leftrightarrow & \color{red}{836} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{836} & & \\ & V = \left\{ \frac{-39}{836} \right\} & \\\end{align}\)
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