Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 12x-\frac{24}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-72} & = & \color{red}{-165x} +22 \\\Leftrightarrow & 396x \color{red}{-72} \color{blue}{+72} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+72} \\\Leftrightarrow & 396x+165x& = & 22+72 \\\Leftrightarrow & \color{red}{561} x& = & 94 \\\Leftrightarrow & x = \frac{94}{561} & & \\ & V = \left\{ \frac{94}{561} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{+16} & = & \color{red}{154x} +33 \\\Leftrightarrow & 440x \color{red}{+16} \color{blue}{-16} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{-16} \\\Leftrightarrow & 440x-154x& = & 33-16 \\\Leftrightarrow & \color{red}{286} x& = & 17 \\\Leftrightarrow & x = \frac{17}{286} & & \\ & V = \left\{ \frac{17}{286} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 8x+\frac{4}{5} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 8x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+70} & = & \color{red}{120x} +12 \\\Leftrightarrow & 315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +12 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & 315x-120x& = & 12-70 \\\Leftrightarrow & \color{red}{195} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{195} & & \\ & V = \left\{ \frac{-58}{195} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & 7x+\frac{3}{4} \\\Leftrightarrow & 10x-\frac{20}{3}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{-80} & = & \color{red}{84x} +9 \\\Leftrightarrow & 120x \color{red}{-80} \color{blue}{+80} \color{blue}{-84x} & = & \color{red}{84x} +9 \color{blue}{-84x} \color{blue}{+80} \\\Leftrightarrow & 120x-84x& = & 9+80 \\\Leftrightarrow & \color{red}{36} x& = & 89 \\\Leftrightarrow & x = \frac{89}{36} & & \\ & V = \left\{ \frac{89}{36} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{11})& = & 7x+\frac{7}{3} \\\Leftrightarrow & 15x+\frac{12}{11}& = & 7x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+36} & = & \color{red}{231x} +77 \\\Leftrightarrow & 495x \color{red}{+36} \color{blue}{-36} \color{blue}{-231x} & = & \color{red}{231x} +77 \color{blue}{-231x} \color{blue}{-36} \\\Leftrightarrow & 495x-231x& = & 77-36 \\\Leftrightarrow & \color{red}{264} x& = & 41 \\\Leftrightarrow & x = \frac{41}{264} & & \\ & V = \left\{ \frac{41}{264} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 2x+\frac{2}{7} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 2x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1176}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{112}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1176x \color{red}{-147} & = & \color{red}{112x} +16 \\\Leftrightarrow & 1176x \color{red}{-147} \color{blue}{+147} \color{blue}{-112x} & = & \color{red}{112x} +16 \color{blue}{-112x} \color{blue}{+147} \\\Leftrightarrow & 1176x-112x& = & 16+147 \\\Leftrightarrow & \color{red}{1064} x& = & 163 \\\Leftrightarrow & x = \frac{163}{1064} & & \\ & V = \left\{ \frac{163}{1064} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{10})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -15x+\frac{9}{10}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-880}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{+99} & = & \color{red}{-880x} +60 \\\Leftrightarrow & -1650x \color{red}{+99} \color{blue}{-99} \color{blue}{+880x} & = & \color{red}{-880x} +60 \color{blue}{+880x} \color{blue}{-99} \\\Leftrightarrow & -1650x+880x& = & 60-99 \\\Leftrightarrow & \color{red}{-770} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-770} & & \\\Leftrightarrow & x = \frac{39}{770} & & \\ & V = \left\{ \frac{39}{770} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{7})& = & 4x+\frac{3}{11} \\\Leftrightarrow & -15x+\frac{12}{7}& = & 4x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{132}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+132} & = & \color{red}{308x} +21 \\\Leftrightarrow & -1155x \color{red}{+132} \color{blue}{-132} \color{blue}{-308x} & = & \color{red}{308x} +21 \color{blue}{-308x} \color{blue}{-132} \\\Leftrightarrow & -1155x-308x& = & 21-132 \\\Leftrightarrow & \color{red}{-1463} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{-1463} & & \\\Leftrightarrow & x = \frac{111}{1463} & & \\ & V = \left\{ \frac{111}{1463} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 18x+\frac{30}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+330} & = & \color{red}{-385x} +42 \\\Leftrightarrow & 1386x \color{red}{+330} \color{blue}{-330} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{-330} \\\Leftrightarrow & 1386x+385x& = & 42-330 \\\Leftrightarrow & \color{red}{1771} x& = & -288 \\\Leftrightarrow & x = \frac{-288}{1771} & & \\ & V = \left\{ \frac{-288}{1771} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{6}{11}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{-30} & = & \color{red}{440x} +66 \\\Leftrightarrow & -825x \color{red}{-30} \color{blue}{+30} \color{blue}{-440x} & = & \color{red}{440x} +66 \color{blue}{-440x} \color{blue}{+30} \\\Leftrightarrow & -825x-440x& = & 66+30 \\\Leftrightarrow & \color{red}{-1265} x& = & 96 \\\Leftrightarrow & x = \frac{96}{-1265} & & \\\Leftrightarrow & x = \frac{-96}{1265} & & \\ & V = \left\{ \frac{-96}{1265} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-50} & = & \color{red}{280x} +14 \\\Leftrightarrow & -525x \color{red}{-50} \color{blue}{+50} \color{blue}{-280x} & = & \color{red}{280x} +14 \color{blue}{-280x} \color{blue}{+50} \\\Leftrightarrow & -525x-280x& = & 14+50 \\\Leftrightarrow & \color{red}{-805} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-805} & & \\\Leftrightarrow & x = \frac{-64}{805} & & \\ & V = \left\{ \frac{-64}{805} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{11})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x- \frac{24}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{33}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{-24} & = & \color{red}{-308x} +33 \\\Leftrightarrow & -264x \color{red}{-24} \color{blue}{+24} \color{blue}{+308x} & = & \color{red}{-308x} +33 \color{blue}{+308x} \color{blue}{+24} \\\Leftrightarrow & -264x+308x& = & 33+24 \\\Leftrightarrow & \color{red}{44} x& = & 57 \\\Leftrightarrow & x = \frac{57}{44} & & \\ & V = \left\{ \frac{57}{44} \right\} & \\\end{align}\)
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