Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -7x+\frac{3}{8} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -7x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{+64} & = & \color{red}{-392x} +21 \\\Leftrightarrow & 672x \color{red}{+64} \color{blue}{-64} \color{blue}{+392x} & = & \color{red}{-392x} +21 \color{blue}{+392x} \color{blue}{-64} \\\Leftrightarrow & 672x+392x& = & 21-64 \\\Leftrightarrow & \color{red}{1064} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{1064} & & \\ & V = \left\{ \frac{-43}{1064} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & -2x+\frac{5}{4} \\\Leftrightarrow & 15x-\frac{6}{7}& = & -2x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-56}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-24} & = & \color{red}{-56x} +35 \\\Leftrightarrow & 420x \color{red}{-24} \color{blue}{+24} \color{blue}{+56x} & = & \color{red}{-56x} +35 \color{blue}{+56x} \color{blue}{+24} \\\Leftrightarrow & 420x+56x& = & 35+24 \\\Leftrightarrow & \color{red}{476} x& = & 59 \\\Leftrightarrow & x = \frac{59}{476} & & \\ & V = \left\{ \frac{59}{476} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{3}{4})& = & 2x+\frac{3}{7} \\\Leftrightarrow & 25x+\frac{15}{4}& = & 2x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{105}{ \color{blue}{28} })& = & (\frac{56}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+105} & = & \color{red}{56x} +12 \\\Leftrightarrow & 700x \color{red}{+105} \color{blue}{-105} \color{blue}{-56x} & = & \color{red}{56x} +12 \color{blue}{-56x} \color{blue}{-105} \\\Leftrightarrow & 700x-56x& = & 12-105 \\\Leftrightarrow & \color{red}{644} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{644} & & \\ & V = \left\{ \frac{-93}{644} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{4})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{15}{4}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+45} & = & \color{red}{84x} +16 \\\Leftrightarrow & 180x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +16 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & 180x-84x& = & 16-45 \\\Leftrightarrow & \color{red}{96} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{96} & & \\ & V = \left\{ \frac{-29}{96} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{270}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 270x \color{red}{-36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 270x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 270x+75x& = & 20+36 \\\Leftrightarrow & \color{red}{345} x& = & 56 \\\Leftrightarrow & x = \frac{56}{345} & & \\ & V = \left\{ \frac{56}{345} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{3}{7})& = & -7x+\frac{2}{7} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+6} & = & \color{red}{-49x} +2 \\\Leftrightarrow & 70x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +2 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & 70x+49x& = & 2-6 \\\Leftrightarrow & \color{red}{119} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{119} & & \\ & V = \left\{ \frac{-4}{119} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 30x-\frac{24}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{168}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-168} & = & \color{red}{245x} +50 \\\Leftrightarrow & 1050x \color{red}{-168} \color{blue}{+168} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{+168} \\\Leftrightarrow & 1050x-245x& = & 50+168 \\\Leftrightarrow & \color{red}{805} x& = & 218 \\\Leftrightarrow & x = \frac{218}{805} & & \\ & V = \left\{ \frac{218}{805} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{8}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{56}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-56} & = & \color{red}{-245x} +30 \\\Leftrightarrow & -350x \color{red}{-56} \color{blue}{+56} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{+56} \\\Leftrightarrow & -350x+245x& = & 30+56 \\\Leftrightarrow & \color{red}{-105} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-105} & & \\\Leftrightarrow & x = \frac{-86}{105} & & \\ & V = \left\{ \frac{-86}{105} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{5}{7})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 10x-\frac{10}{7}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{-10} & = & \color{red}{49x} +6 \\\Leftrightarrow & 70x \color{red}{-10} \color{blue}{+10} \color{blue}{-49x} & = & \color{red}{49x} +6 \color{blue}{-49x} \color{blue}{+10} \\\Leftrightarrow & 70x-49x& = & 6+10 \\\Leftrightarrow & \color{red}{21} x& = & 16 \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{5}{3})& = & -2x+\frac{4}{9} \\\Leftrightarrow & 21x-\frac{35}{3}& = & -2x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{189}{ \color{blue}{9} }x- \frac{105}{ \color{blue}{9} })& = & (\frac{-18}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 189x \color{red}{-105} & = & \color{red}{-18x} +4 \\\Leftrightarrow & 189x \color{red}{-105} \color{blue}{+105} \color{blue}{+18x} & = & \color{red}{-18x} +4 \color{blue}{+18x} \color{blue}{+105} \\\Leftrightarrow & 189x+18x& = & 4+105 \\\Leftrightarrow & \color{red}{207} x& = & 109 \\\Leftrightarrow & x = \frac{109}{207} & & \\ & V = \left\{ \frac{109}{207} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{1260}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 1260x \color{red}{+180} & = & \color{red}{-294x} +35 \\\Leftrightarrow & 1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{-180} \\\Leftrightarrow & 1260x+294x& = & 35-180 \\\Leftrightarrow & \color{red}{1554} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{1554} & & \\ & V = \left\{ \frac{-145}{1554} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 6x-\frac{8}{3}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{36}{ \color{blue}{6} }x- \frac{16}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 36x \color{red}{-16} & = & \color{red}{-30x} +15 \\\Leftrightarrow & 36x \color{red}{-16} \color{blue}{+16} \color{blue}{+30x} & = & \color{red}{-30x} +15 \color{blue}{+30x} \color{blue}{+16} \\\Leftrightarrow & 36x+30x& = & 15+16 \\\Leftrightarrow & \color{red}{66} x& = & 31 \\\Leftrightarrow & x = \frac{31}{66} & & \\ & V = \left\{ \frac{31}{66} \right\} & \\\end{align}\)
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