Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & -8x+\frac{9}{4} \\\Leftrightarrow & 9x+\frac{6}{5}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+24} & = & \color{red}{-160x} +45 \\\Leftrightarrow & 180x \color{red}{+24} \color{blue}{-24} \color{blue}{+160x} & = & \color{red}{-160x} +45 \color{blue}{+160x} \color{blue}{-24} \\\Leftrightarrow & 180x+160x& = & 45-24 \\\Leftrightarrow & \color{red}{340} x& = & 21 \\\Leftrightarrow & x = \frac{21}{340} & & \\ & V = \left\{ \frac{21}{340} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{5}{3})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x+ \frac{60}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{+60} & = & \color{red}{-45x} +2 \\\Leftrightarrow & -108x \color{red}{+60} \color{blue}{-60} \color{blue}{+45x} & = & \color{red}{-45x} +2 \color{blue}{+45x} \color{blue}{-60} \\\Leftrightarrow & -108x+45x& = & 2-60 \\\Leftrightarrow & \color{red}{-63} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{-63} & & \\\Leftrightarrow & x = \frac{58}{63} & & \\ & V = \left\{ \frac{58}{63} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{5})& = & 5x+\frac{5}{7} \\\Leftrightarrow & 6x+\frac{6}{5}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+42} & = & \color{red}{175x} +25 \\\Leftrightarrow & 210x \color{red}{+42} \color{blue}{-42} \color{blue}{-175x} & = & \color{red}{175x} +25 \color{blue}{-175x} \color{blue}{-42} \\\Leftrightarrow & 210x-175x& = & 25-42 \\\Leftrightarrow & \color{red}{35} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{35} & & \\ & V = \left\{ \frac{-17}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{11})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-50} & = & \color{red}{-385x} +33 \\\Leftrightarrow & -550x \color{red}{-50} \color{blue}{+50} \color{blue}{+385x} & = & \color{red}{-385x} +33 \color{blue}{+385x} \color{blue}{+50} \\\Leftrightarrow & -550x+385x& = & 33+50 \\\Leftrightarrow & \color{red}{-165} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-165} & & \\\Leftrightarrow & x = \frac{-83}{165} & & \\ & V = \left\{ \frac{-83}{165} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-147x} +56 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & 420x+147x& = & 56+60 \\\Leftrightarrow & \color{red}{567} x& = & 116 \\\Leftrightarrow & x = \frac{116}{567} & & \\ & V = \left\{ \frac{116}{567} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{4}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 10x+\frac{8}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{+8} & = & \color{red}{-9x} +8 \\\Leftrightarrow & 30x \color{red}{+8} \color{blue}{-8} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{-8} \\\Leftrightarrow & 30x+9x& = & 8-8 \\\Leftrightarrow & \color{red}{39} x& = & 0 \\\Leftrightarrow & x = \frac{0}{39} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{16}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{32}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-32} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 264x \color{red}{-32} \color{blue}{+32} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+32} \\\Leftrightarrow & 264x+110x& = & 99+32 \\\Leftrightarrow & \color{red}{374} x& = & 131 \\\Leftrightarrow & x = \frac{131}{374} & & \\ & V = \left\{ \frac{131}{374} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{7})& = & 2x+\frac{7}{11} \\\Leftrightarrow & 15x-\frac{9}{7}& = & 2x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-99} & = & \color{red}{154x} +49 \\\Leftrightarrow & 1155x \color{red}{-99} \color{blue}{+99} \color{blue}{-154x} & = & \color{red}{154x} +49 \color{blue}{-154x} \color{blue}{+99} \\\Leftrightarrow & 1155x-154x& = & 49+99 \\\Leftrightarrow & \color{red}{1001} x& = & 148 \\\Leftrightarrow & x = \frac{148}{1001} & & \\ & V = \left\{ \frac{148}{1001} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 24x-\frac{18}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1848}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1848x \color{red}{-126} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 1848x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & 1848x+385x& = & 22+126 \\\Leftrightarrow & \color{red}{2233} x& = & 148 \\\Leftrightarrow & x = \frac{148}{2233} & & \\ & V = \left\{ \frac{148}{2233} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-30} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 525x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & 525x+245x& = & 42+30 \\\Leftrightarrow & \color{red}{770} x& = & 72 \\\Leftrightarrow & x = \frac{72}{770} & & \\\Leftrightarrow & x = \frac{36}{385} & & \\ & V = \left\{ \frac{36}{385} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{2}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{14}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{+14} & = & \color{red}{27x} +10 \\\Leftrightarrow & 84x \color{red}{+14} \color{blue}{-14} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-14} \\\Leftrightarrow & 84x-27x& = & 10-14 \\\Leftrightarrow & \color{red}{57} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{57} & & \\ & V = \left\{ \frac{-4}{57} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 10x+\frac{4}{5}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+44} & = & \color{red}{-165x} +30 \\\Leftrightarrow & 550x \color{red}{+44} \color{blue}{-44} \color{blue}{+165x} & = & \color{red}{-165x} +30 \color{blue}{+165x} \color{blue}{-44} \\\Leftrightarrow & 550x+165x& = & 30-44 \\\Leftrightarrow & \color{red}{715} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{715} & & \\ & V = \left\{ \frac{-14}{715} \right\} & \\\end{align}\)
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