Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{4}{5})& = & 9x+\frac{5}{8} \\\Leftrightarrow & -35x+\frac{28}{5}& = & 9x+\frac{5}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{224}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{25}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+224} & = & \color{red}{360x} +25 \\\Leftrightarrow & -1400x \color{red}{+224} \color{blue}{-224} \color{blue}{-360x} & = & \color{red}{360x} +25 \color{blue}{-360x} \color{blue}{-224} \\\Leftrightarrow & -1400x-360x& = & 25-224 \\\Leftrightarrow & \color{red}{-1760} x& = & -199 \\\Leftrightarrow & x = \frac{-199}{-1760} & & \\\Leftrightarrow & x = \frac{199}{1760} & & \\ & V = \left\{ \frac{199}{1760} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-120} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 990x \color{red}{-120} \color{blue}{+120} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+120} \\\Leftrightarrow & 990x+275x& = & 66+120 \\\Leftrightarrow & \color{red}{1265} x& = & 186 \\\Leftrightarrow & x = \frac{186}{1265} & & \\ & V = \left\{ \frac{186}{1265} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{5})& = & -7x+\frac{3}{10} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{+8} & = & \color{red}{-70x} +3 \\\Leftrightarrow & -100x \color{red}{+8} \color{blue}{-8} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-8} \\\Leftrightarrow & -100x+70x& = & 3-8 \\\Leftrightarrow & \color{red}{-30} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-30} & & \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{8}{5} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{175}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-175} & = & \color{red}{120x} +24 \\\Leftrightarrow & -315x \color{red}{-175} \color{blue}{+175} \color{blue}{-120x} & = & \color{red}{120x} +24 \color{blue}{-120x} \color{blue}{+175} \\\Leftrightarrow & -315x-120x& = & 24+175 \\\Leftrightarrow & \color{red}{-435} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-435} & & \\\Leftrightarrow & x = \frac{-199}{435} & & \\ & V = \left\{ \frac{-199}{435} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & -9x+\frac{10}{3} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -9x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+48} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 336x \color{red}{+48} \color{blue}{-48} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{-48} \\\Leftrightarrow & 336x+189x& = & 70-48 \\\Leftrightarrow & \color{red}{525} x& = & 22 \\\Leftrightarrow & x = \frac{22}{525} & & \\ & V = \left\{ \frac{22}{525} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{5})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -28x-\frac{28}{5}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-308} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -1540x \color{red}{-308} \color{blue}{+308} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+308} \\\Leftrightarrow & -1540x+385x& = & 35+308 \\\Leftrightarrow & \color{red}{-1155} x& = & 343 \\\Leftrightarrow & x = \frac{343}{-1155} & & \\\Leftrightarrow & x = \frac{-49}{165} & & \\ & V = \left\{ \frac{-49}{165} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{7})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -15x+\frac{9}{7}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+45} & = & \color{red}{280x} +42 \\\Leftrightarrow & -525x \color{red}{+45} \color{blue}{-45} \color{blue}{-280x} & = & \color{red}{280x} +42 \color{blue}{-280x} \color{blue}{-45} \\\Leftrightarrow & -525x-280x& = & 42-45 \\\Leftrightarrow & \color{red}{-805} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{-805} & & \\\Leftrightarrow & x = \frac{3}{805} & & \\ & V = \left\{ \frac{3}{805} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+63} & = & \color{red}{-99x} +22 \\\Leftrightarrow & 462x \color{red}{+63} \color{blue}{-63} \color{blue}{+99x} & = & \color{red}{-99x} +22 \color{blue}{+99x} \color{blue}{-63} \\\Leftrightarrow & 462x+99x& = & 22-63 \\\Leftrightarrow & \color{red}{561} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{561} & & \\ & V = \left\{ \frac{-41}{561} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & -7x+\frac{4}{7} \\\Leftrightarrow & -6x-\frac{4}{5}& = & -7x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-28} & = & \color{red}{-245x} +20 \\\Leftrightarrow & -210x \color{red}{-28} \color{blue}{+28} \color{blue}{+245x} & = & \color{red}{-245x} +20 \color{blue}{+245x} \color{blue}{+28} \\\Leftrightarrow & -210x+245x& = & 20+28 \\\Leftrightarrow & \color{red}{35} x& = & 48 \\\Leftrightarrow & x = \frac{48}{35} & & \\ & V = \left\{ \frac{48}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x-\frac{10}{3}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-18}{ \color{blue}{3} }x- \frac{10}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -18x \color{red}{-10} & = & \color{red}{-21x} +10 \\\Leftrightarrow & -18x \color{red}{-10} \color{blue}{+10} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{+10} \\\Leftrightarrow & -18x+21x& = & 10+10 \\\Leftrightarrow & \color{red}{3} x& = & 20 \\\Leftrightarrow & x = \frac{20}{3} & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{4})& = & -6x+\frac{10}{7} \\\Leftrightarrow & -35x-\frac{21}{4}& = & -6x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-980}{ \color{blue}{28} }x- \frac{147}{ \color{blue}{28} })& = & (\frac{-168}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -980x \color{red}{-147} & = & \color{red}{-168x} +40 \\\Leftrightarrow & -980x \color{red}{-147} \color{blue}{+147} \color{blue}{+168x} & = & \color{red}{-168x} +40 \color{blue}{+168x} \color{blue}{+147} \\\Leftrightarrow & -980x+168x& = & 40+147 \\\Leftrightarrow & \color{red}{-812} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-812} & & \\\Leftrightarrow & x = \frac{-187}{812} & & \\ & V = \left\{ \frac{-187}{812} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x+\frac{24}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x+ \frac{72}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{+72} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -630x \color{red}{+72} \color{blue}{-72} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-72} \\\Leftrightarrow & -630x+147x& = & 28-72 \\\Leftrightarrow & \color{red}{-483} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{-483} & & \\\Leftrightarrow & x = \frac{44}{483} & & \\ & V = \left\{ \frac{44}{483} \right\} & \\\end{align}\)
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