Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{4}{9})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{63x} +12 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+8} \\\Leftrightarrow & -90x-63x& = & 12+8 \\\Leftrightarrow & \color{red}{-153} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-153} & & \\\Leftrightarrow & x = \frac{-20}{153} & & \\ & V = \left\{ \frac{-20}{153} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{11})& = & 8x+\frac{6}{5} \\\Leftrightarrow & -18x+\frac{30}{11}& = & 8x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+150} & = & \color{red}{440x} +66 \\\Leftrightarrow & -990x \color{red}{+150} \color{blue}{-150} \color{blue}{-440x} & = & \color{red}{440x} +66 \color{blue}{-440x} \color{blue}{-150} \\\Leftrightarrow & -990x-440x& = & 66-150 \\\Leftrightarrow & \color{red}{-1430} x& = & -84 \\\Leftrightarrow & x = \frac{-84}{-1430} & & \\\Leftrightarrow & x = \frac{42}{715} & & \\ & V = \left\{ \frac{42}{715} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{5})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -8x-\frac{6}{5}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{-12} & = & \color{red}{90x} +15 \\\Leftrightarrow & -80x \color{red}{-12} \color{blue}{+12} \color{blue}{-90x} & = & \color{red}{90x} +15 \color{blue}{-90x} \color{blue}{+12} \\\Leftrightarrow & -80x-90x& = & 15+12 \\\Leftrightarrow & \color{red}{-170} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-170} & & \\\Leftrightarrow & x = \frac{-27}{170} & & \\ & V = \left\{ \frac{-27}{170} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{5}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-504}{ \color{blue}{28} }x+ \frac{120}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -504x \color{red}{+120} & = & \color{red}{-84x} +21 \\\Leftrightarrow & -504x \color{red}{+120} \color{blue}{-120} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{-120} \\\Leftrightarrow & -504x+84x& = & 21-120 \\\Leftrightarrow & \color{red}{-420} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{-420} & & \\\Leftrightarrow & x = \frac{33}{140} & & \\ & V = \left\{ \frac{33}{140} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{11})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -21x-\frac{21}{11}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x- \frac{189}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{-189} & = & \color{red}{-792x} +88 \\\Leftrightarrow & -2079x \color{red}{-189} \color{blue}{+189} \color{blue}{+792x} & = & \color{red}{-792x} +88 \color{blue}{+792x} \color{blue}{+189} \\\Leftrightarrow & -2079x+792x& = & 88+189 \\\Leftrightarrow & \color{red}{-1287} x& = & 277 \\\Leftrightarrow & x = \frac{277}{-1287} & & \\\Leftrightarrow & x = \frac{-277}{1287} & & \\ & V = \left\{ \frac{-277}{1287} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+1)& = & 7x+\frac{3}{4} \\\Leftrightarrow & -25x-5& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-100}{ \color{blue}{4} }x- \frac{20}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -100x \color{red}{-20} & = & \color{red}{28x} +3 \\\Leftrightarrow & -100x \color{red}{-20} \color{blue}{+20} \color{blue}{-28x} & = & \color{red}{28x} +3 \color{blue}{-28x} \color{blue}{+20} \\\Leftrightarrow & -100x-28x& = & 3+20 \\\Leftrightarrow & \color{red}{-128} x& = & 23 \\\Leftrightarrow & x = \frac{23}{-128} & & \\\Leftrightarrow & x = \frac{-23}{128} & & \\ & V = \left\{ \frac{-23}{128} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -20x+\frac{20}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{100}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+100} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -700x \color{red}{+100} \color{blue}{-100} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{-100} \\\Leftrightarrow & -700x+245x& = & 14-100 \\\Leftrightarrow & \color{red}{-455} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{-455} & & \\\Leftrightarrow & x = \frac{86}{455} & & \\ & V = \left\{ \frac{86}{455} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 9x+\frac{6}{7} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1260}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1260x \color{red}{-56} & = & \color{red}{567x} +54 \\\Leftrightarrow & -1260x \color{red}{-56} \color{blue}{+56} \color{blue}{-567x} & = & \color{red}{567x} +54 \color{blue}{-567x} \color{blue}{+56} \\\Leftrightarrow & -1260x-567x& = & 54+56 \\\Leftrightarrow & \color{red}{-1827} x& = & 110 \\\Leftrightarrow & x = \frac{110}{-1827} & & \\\Leftrightarrow & x = \frac{-110}{1827} & & \\ & V = \left\{ \frac{-110}{1827} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{3}{5})& = & 3x+\frac{3}{7} \\\Leftrightarrow & -20x+\frac{12}{5}& = & 3x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{+84} & = & \color{red}{105x} +15 \\\Leftrightarrow & -700x \color{red}{+84} \color{blue}{-84} \color{blue}{-105x} & = & \color{red}{105x} +15 \color{blue}{-105x} \color{blue}{-84} \\\Leftrightarrow & -700x-105x& = & 15-84 \\\Leftrightarrow & \color{red}{-805} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-805} & & \\\Leftrightarrow & x = \frac{3}{35} & & \\ & V = \left\{ \frac{3}{35} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -16x+\frac{20}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1008}{ \color{blue}{63} }x+ \frac{180}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1008x \color{red}{+180} & = & \color{red}{441x} +14 \\\Leftrightarrow & -1008x \color{red}{+180} \color{blue}{-180} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{-180} \\\Leftrightarrow & -1008x-441x& = & 14-180 \\\Leftrightarrow & \color{red}{-1449} x& = & -166 \\\Leftrightarrow & x = \frac{-166}{-1449} & & \\\Leftrightarrow & x = \frac{166}{1449} & & \\ & V = \left\{ \frac{166}{1449} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{15}{4}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-75} & = & \color{red}{-100x} +6 \\\Leftrightarrow & -240x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +6 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & -240x+100x& = & 6+75 \\\Leftrightarrow & \color{red}{-140} x& = & 81 \\\Leftrightarrow & x = \frac{81}{-140} & & \\\Leftrightarrow & x = \frac{-81}{140} & & \\ & V = \left\{ \frac{-81}{140} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{11})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 16x-\frac{8}{11}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{-8} & = & \color{red}{-55x} +8 \\\Leftrightarrow & 176x \color{red}{-8} \color{blue}{+8} \color{blue}{+55x} & = & \color{red}{-55x} +8 \color{blue}{+55x} \color{blue}{+8} \\\Leftrightarrow & 176x+55x& = & 8+8 \\\Leftrightarrow & \color{red}{231} x& = & 16 \\\Leftrightarrow & x = \frac{16}{231} & & \\ & V = \left\{ \frac{16}{231} \right\} & \\\end{align}\)
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