Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-18} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -330x \color{red}{-18} \color{blue}{+18} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+18} \\\Leftrightarrow & -330x+77x& = & 6+18 \\\Leftrightarrow & \color{red}{-253} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-253} & & \\\Leftrightarrow & x = \frac{-24}{253} & & \\ & V = \left\{ \frac{-24}{253} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{8}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+24} & = & \color{red}{147x} +56 \\\Leftrightarrow & -126x \color{red}{+24} \color{blue}{-24} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{-24} \\\Leftrightarrow & -126x-147x& = & 56-24 \\\Leftrightarrow & \color{red}{-273} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-273} & & \\\Leftrightarrow & x = \frac{-32}{273} & & \\ & V = \left\{ \frac{-32}{273} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{8})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{21}{8}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-672}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -672x \color{red}{+63} & = & \color{red}{-192x} +80 \\\Leftrightarrow & -672x \color{red}{+63} \color{blue}{-63} \color{blue}{+192x} & = & \color{red}{-192x} +80 \color{blue}{+192x} \color{blue}{-63} \\\Leftrightarrow & -672x+192x& = & 80-63 \\\Leftrightarrow & \color{red}{-480} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-480} & & \\\Leftrightarrow & x = \frac{-17}{480} & & \\ & V = \left\{ \frac{-17}{480} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 30x-\frac{12}{5}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{25}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-84} & = & \color{red}{-245x} +25 \\\Leftrightarrow & 1050x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +25 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 1050x+245x& = & 25+84 \\\Leftrightarrow & \color{red}{1295} x& = & 109 \\\Leftrightarrow & x = \frac{109}{1295} & & \\ & V = \left\{ \frac{109}{1295} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+30} & = & \color{red}{315x} +42 \\\Leftrightarrow & 280x \color{red}{+30} \color{blue}{-30} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{-30} \\\Leftrightarrow & 280x-315x& = & 42-30 \\\Leftrightarrow & \color{red}{-35} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-35} & & \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{8}{3}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+40} & = & \color{red}{135x} +18 \\\Leftrightarrow & -120x \color{red}{+40} \color{blue}{-40} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{-40} \\\Leftrightarrow & -120x-135x& = & 18-40 \\\Leftrightarrow & \color{red}{-255} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-255} & & \\\Leftrightarrow & x = \frac{22}{255} & & \\ & V = \left\{ \frac{22}{255} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{5}{3})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -20x-\frac{20}{3}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-140} & = & \color{red}{-147x} +24 \\\Leftrightarrow & -420x \color{red}{-140} \color{blue}{+140} \color{blue}{+147x} & = & \color{red}{-147x} +24 \color{blue}{+147x} \color{blue}{+140} \\\Leftrightarrow & -420x+147x& = & 24+140 \\\Leftrightarrow & \color{red}{-273} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-273} & & \\\Leftrightarrow & x = \frac{-164}{273} & & \\ & V = \left\{ \frac{-164}{273} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{11})& = & -3x+\frac{5}{3} \\\Leftrightarrow & 35x+\frac{21}{11}& = & -3x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+63} & = & \color{red}{-99x} +55 \\\Leftrightarrow & 1155x \color{red}{+63} \color{blue}{-63} \color{blue}{+99x} & = & \color{red}{-99x} +55 \color{blue}{+99x} \color{blue}{-63} \\\Leftrightarrow & 1155x+99x& = & 55-63 \\\Leftrightarrow & \color{red}{1254} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{1254} & & \\\Leftrightarrow & x = \frac{-4}{627} & & \\ & V = \left\{ \frac{-4}{627} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{6})& = & -3x+\frac{10}{11} \\\Leftrightarrow & -35x+\frac{35}{6}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 6 en 11 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-2310}{ \color{blue}{66} }x+ \frac{385}{ \color{blue}{66} })& = & (\frac{-198}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -2310x \color{red}{+385} & = & \color{red}{-198x} +60 \\\Leftrightarrow & -2310x \color{red}{+385} \color{blue}{-385} \color{blue}{+198x} & = & \color{red}{-198x} +60 \color{blue}{+198x} \color{blue}{-385} \\\Leftrightarrow & -2310x+198x& = & 60-385 \\\Leftrightarrow & \color{red}{-2112} x& = & -325 \\\Leftrightarrow & x = \frac{-325}{-2112} & & \\\Leftrightarrow & x = \frac{325}{2112} & & \\ & V = \left\{ \frac{325}{2112} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{5})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -28x+\frac{21}{5}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-980}{ \color{blue}{35} }x+ \frac{147}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -980x \color{red}{+147} & = & \color{red}{245x} +30 \\\Leftrightarrow & -980x \color{red}{+147} \color{blue}{-147} \color{blue}{-245x} & = & \color{red}{245x} +30 \color{blue}{-245x} \color{blue}{-147} \\\Leftrightarrow & -980x-245x& = & 30-147 \\\Leftrightarrow & \color{red}{-1225} x& = & -117 \\\Leftrightarrow & x = \frac{-117}{-1225} & & \\\Leftrightarrow & x = \frac{117}{1225} & & \\ & V = \left\{ \frac{117}{1225} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{15}{2}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{75}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+75} & = & \color{red}{70x} +12 \\\Leftrightarrow & -100x \color{red}{+75} \color{blue}{-75} \color{blue}{-70x} & = & \color{red}{70x} +12 \color{blue}{-70x} \color{blue}{-75} \\\Leftrightarrow & -100x-70x& = & 12-75 \\\Leftrightarrow & \color{red}{-170} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-170} & & \\\Leftrightarrow & x = \frac{63}{170} & & \\ & V = \left\{ \frac{63}{170} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{3}{5})& = & -3x+\frac{4}{5} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -100x \color{red}{-12} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -100x \color{red}{-12} \color{blue}{+12} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+12} \\\Leftrightarrow & -100x+15x& = & 4+12 \\\Leftrightarrow & \color{red}{-85} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-85} & & \\\Leftrightarrow & x = \frac{-16}{85} & & \\ & V = \left\{ \frac{-16}{85} \right\} & \\\end{align}\)
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