Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-66} & = & \color{red}{154x} +21 \\\Leftrightarrow & 1155x \color{red}{-66} \color{blue}{+66} \color{blue}{-154x} & = & \color{red}{154x} +21 \color{blue}{-154x} \color{blue}{+66} \\\Leftrightarrow & 1155x-154x& = & 21+66 \\\Leftrightarrow & \color{red}{1001} x& = & 87 \\\Leftrightarrow & x = \frac{87}{1001} & & \\ & V = \left\{ \frac{87}{1001} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{3})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{16}{3}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{-16} & = & \color{red}{-9x} +8 \\\Leftrightarrow & -24x \color{red}{-16} \color{blue}{+16} \color{blue}{+9x} & = & \color{red}{-9x} +8 \color{blue}{+9x} \color{blue}{+16} \\\Leftrightarrow & -24x+9x& = & 8+16 \\\Leftrightarrow & \color{red}{-15} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-15} & & \\\Leftrightarrow & x = \frac{-8}{5} & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{3}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1100}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1100x \color{red}{+132} & = & \color{red}{385x} +20 \\\Leftrightarrow & -1100x \color{red}{+132} \color{blue}{-132} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{-132} \\\Leftrightarrow & -1100x-385x& = & 20-132 \\\Leftrightarrow & \color{red}{-1485} x& = & -112 \\\Leftrightarrow & x = \frac{-112}{-1485} & & \\\Leftrightarrow & x = \frac{112}{1485} & & \\ & V = \left\{ \frac{112}{1485} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{3})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -8x+\frac{16}{3}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+80} & = & \color{red}{-135x} +18 \\\Leftrightarrow & -120x \color{red}{+80} \color{blue}{-80} \color{blue}{+135x} & = & \color{red}{-135x} +18 \color{blue}{+135x} \color{blue}{-80} \\\Leftrightarrow & -120x+135x& = & 18-80 \\\Leftrightarrow & \color{red}{15} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{15} & & \\ & V = \left\{ \frac{-62}{15} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{5}{3} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-24}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -24x \color{red}{+20} & = & \color{red}{27x} +5 \\\Leftrightarrow & -24x \color{red}{+20} \color{blue}{-20} \color{blue}{-27x} & = & \color{red}{27x} +5 \color{blue}{-27x} \color{blue}{-20} \\\Leftrightarrow & -24x-27x& = & 5-20 \\\Leftrightarrow & \color{red}{-51} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-51} & & \\\Leftrightarrow & x = \frac{5}{17} & & \\ & V = \left\{ \frac{5}{17} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{5})& = & 3x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{12}{5}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+84} & = & \color{red}{105x} +10 \\\Leftrightarrow & -280x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +10 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & -280x-105x& = & 10-84 \\\Leftrightarrow & \color{red}{-385} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-385} & & \\\Leftrightarrow & x = \frac{74}{385} & & \\ & V = \left\{ \frac{74}{385} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+54} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 990x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & 990x+231x& = & 22-54 \\\Leftrightarrow & \color{red}{1221} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{1221} & & \\ & V = \left\{ \frac{-32}{1221} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -30x+\frac{24}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x+ \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{+168} & = & \color{red}{245x} +50 \\\Leftrightarrow & -1050x \color{red}{+168} \color{blue}{-168} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-168} \\\Leftrightarrow & -1050x-245x& = & 50-168 \\\Leftrightarrow & \color{red}{-1295} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-1295} & & \\\Leftrightarrow & x = \frac{118}{1295} & & \\ & V = \left\{ \frac{118}{1295} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & -8x+\frac{3}{10} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{56}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-80x} +3 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+80x} & = & \color{red}{-80x} +3 \color{blue}{+80x} \color{blue}{+56} \\\Leftrightarrow & 210x+80x& = & 3+56 \\\Leftrightarrow & \color{red}{290} x& = & 59 \\\Leftrightarrow & x = \frac{59}{290} & & \\ & V = \left\{ \frac{59}{290} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 24x+\frac{18}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{+54} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 792x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & 792x+231x& = & 22-54 \\\Leftrightarrow & \color{red}{1023} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{1023} & & \\ & V = \left\{ \frac{-32}{1023} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{4})& = & 3x+\frac{9}{4} \\\Leftrightarrow & 28x+\frac{35}{4}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{112}{ \color{blue}{4} }x+ \frac{35}{ \color{blue}{4} })& = & (\frac{12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 112x \color{red}{+35} & = & \color{red}{12x} +9 \\\Leftrightarrow & 112x \color{red}{+35} \color{blue}{-35} \color{blue}{-12x} & = & \color{red}{12x} +9 \color{blue}{-12x} \color{blue}{-35} \\\Leftrightarrow & 112x-12x& = & 9-35 \\\Leftrightarrow & \color{red}{100} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{100} & & \\\Leftrightarrow & x = \frac{-13}{50} & & \\ & V = \left\{ \frac{-13}{50} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{3})& = & -6x+\frac{8}{11} \\\Leftrightarrow & -35x-\frac{28}{3}& = & -6x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x- \frac{308}{ \color{blue}{33} })& = & (\frac{-198}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{-308} & = & \color{red}{-198x} +24 \\\Leftrightarrow & -1155x \color{red}{-308} \color{blue}{+308} \color{blue}{+198x} & = & \color{red}{-198x} +24 \color{blue}{+198x} \color{blue}{+308} \\\Leftrightarrow & -1155x+198x& = & 24+308 \\\Leftrightarrow & \color{red}{-957} x& = & 332 \\\Leftrightarrow & x = \frac{332}{-957} & & \\\Leftrightarrow & x = \frac{-332}{957} & & \\ & V = \left\{ \frac{-332}{957} \right\} & \\\end{align}\)
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