Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{3}{11} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+18} & = & \color{red}{55x} +3 \\\Leftrightarrow & -132x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +3 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & -132x-55x& = & 3-18 \\\Leftrightarrow & \color{red}{-187} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-187} & & \\\Leftrightarrow & x = \frac{15}{187} & & \\ & V = \left\{ \frac{15}{187} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -12x-\frac{30}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{30}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-30} & = & \color{red}{-55x} +4 \\\Leftrightarrow & -132x \color{red}{-30} \color{blue}{+30} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+30} \\\Leftrightarrow & -132x+55x& = & 4+30 \\\Leftrightarrow & \color{red}{-77} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-77} & & \\\Leftrightarrow & x = \frac{-34}{77} & & \\ & V = \left\{ \frac{-34}{77} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{9})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{10}{9}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+10} & = & \color{red}{63x} +6 \\\Leftrightarrow & 54x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & 54x-63x& = & 6-10 \\\Leftrightarrow & \color{red}{-9} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-9} & & \\\Leftrightarrow & x = \frac{4}{9} & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{5}{12} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{-504}{ \color{blue}{84} }x+ \frac{72}{ \color{blue}{84} })& = & (\frac{588}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & -504x \color{red}{+72} & = & \color{red}{588x} +35 \\\Leftrightarrow & -504x \color{red}{+72} \color{blue}{-72} \color{blue}{-588x} & = & \color{red}{588x} +35 \color{blue}{-588x} \color{blue}{-72} \\\Leftrightarrow & -504x-588x& = & 35-72 \\\Leftrightarrow & \color{red}{-1092} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-1092} & & \\\Leftrightarrow & x = \frac{37}{1092} & & \\ & V = \left\{ \frac{37}{1092} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{3}{4})& = & 4x+\frac{4}{11} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{16}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{+165} & = & \color{red}{176x} +16 \\\Leftrightarrow & 1100x \color{red}{+165} \color{blue}{-165} \color{blue}{-176x} & = & \color{red}{176x} +16 \color{blue}{-176x} \color{blue}{-165} \\\Leftrightarrow & 1100x-176x& = & 16-165 \\\Leftrightarrow & \color{red}{924} x& = & -149 \\\Leftrightarrow & x = \frac{-149}{924} & & \\ & V = \left\{ \frac{-149}{924} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{9})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -10x+\frac{4}{9}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+8} & = & \color{red}{126x} +45 \\\Leftrightarrow & -180x \color{red}{+8} \color{blue}{-8} \color{blue}{-126x} & = & \color{red}{126x} +45 \color{blue}{-126x} \color{blue}{-8} \\\Leftrightarrow & -180x-126x& = & 45-8 \\\Leftrightarrow & \color{red}{-306} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-306} & & \\\Leftrightarrow & x = \frac{-37}{306} & & \\ & V = \left\{ \frac{-37}{306} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{7})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -20x+\frac{16}{7}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+48} & = & \color{red}{-147x} +70 \\\Leftrightarrow & -420x \color{red}{+48} \color{blue}{-48} \color{blue}{+147x} & = & \color{red}{-147x} +70 \color{blue}{+147x} \color{blue}{-48} \\\Leftrightarrow & -420x+147x& = & 70-48 \\\Leftrightarrow & \color{red}{-273} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-273} & & \\\Leftrightarrow & x = \frac{-22}{273} & & \\ & V = \left\{ \frac{-22}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -30x-\frac{18}{11}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x- \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{-162} & = & \color{red}{693x} +88 \\\Leftrightarrow & -2970x \color{red}{-162} \color{blue}{+162} \color{blue}{-693x} & = & \color{red}{693x} +88 \color{blue}{-693x} \color{blue}{+162} \\\Leftrightarrow & -2970x-693x& = & 88+162 \\\Leftrightarrow & \color{red}{-3663} x& = & 250 \\\Leftrightarrow & x = \frac{250}{-3663} & & \\\Leftrightarrow & x = \frac{-250}{3663} & & \\ & V = \left\{ \frac{-250}{3663} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+126} & = & \color{red}{385x} +110 \\\Leftrightarrow & -924x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & -924x-385x& = & 110-126 \\\Leftrightarrow & \color{red}{-1309} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1309} & & \\\Leftrightarrow & x = \frac{16}{1309} & & \\ & V = \left\{ \frac{16}{1309} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{5})& = & 9x+\frac{6}{7} \\\Leftrightarrow & -20x+\frac{8}{5}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+56} & = & \color{red}{315x} +30 \\\Leftrightarrow & -700x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +30 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & -700x-315x& = & 30-56 \\\Leftrightarrow & \color{red}{-1015} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1015} & & \\\Leftrightarrow & x = \frac{26}{1015} & & \\ & V = \left\{ \frac{26}{1015} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{3})& = & -9x+\frac{2}{5} \\\Leftrightarrow & -8x+\frac{4}{3}& = & -9x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+20} & = & \color{red}{-135x} +6 \\\Leftrightarrow & -120x \color{red}{+20} \color{blue}{-20} \color{blue}{+135x} & = & \color{red}{-135x} +6 \color{blue}{+135x} \color{blue}{-20} \\\Leftrightarrow & -120x+135x& = & 6-20 \\\Leftrightarrow & \color{red}{15} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{15} & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-84} & = & \color{red}{175x} +30 \\\Leftrightarrow & -420x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +30 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -420x-175x& = & 30+84 \\\Leftrightarrow & \color{red}{-595} x& = & 114 \\\Leftrightarrow & x = \frac{114}{-595} & & \\\Leftrightarrow & x = \frac{-114}{595} & & \\ & V = \left\{ \frac{-114}{595} \right\} & \\\end{align}\)
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