Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-126} & = & \color{red}{-385x} +22 \\\Leftrightarrow & -924x \color{red}{-126} \color{blue}{+126} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{+126} \\\Leftrightarrow & -924x+385x& = & 22+126 \\\Leftrightarrow & \color{red}{-539} x& = & 148 \\\Leftrightarrow & x = \frac{148}{-539} & & \\\Leftrightarrow & x = \frac{-148}{539} & & \\ & V = \left\{ \frac{-148}{539} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -3x+\frac{5}{4} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -3x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-616}{ \color{blue}{44} }x- \frac{84}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -616x \color{red}{-84} & = & \color{red}{-132x} +55 \\\Leftrightarrow & -616x \color{red}{-84} \color{blue}{+84} \color{blue}{+132x} & = & \color{red}{-132x} +55 \color{blue}{+132x} \color{blue}{+84} \\\Leftrightarrow & -616x+132x& = & 55+84 \\\Leftrightarrow & \color{red}{-484} x& = & 139 \\\Leftrightarrow & x = \frac{139}{-484} & & \\\Leftrightarrow & x = \frac{-139}{484} & & \\ & V = \left\{ \frac{-139}{484} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{5})& = & -7x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{8}{5}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x+ \frac{72}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{+72} & = & \color{red}{-315x} +35 \\\Leftrightarrow & 900x \color{red}{+72} \color{blue}{-72} \color{blue}{+315x} & = & \color{red}{-315x} +35 \color{blue}{+315x} \color{blue}{-72} \\\Leftrightarrow & 900x+315x& = & 35-72 \\\Leftrightarrow & \color{red}{1215} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{1215} & & \\ & V = \left\{ \frac{-37}{1215} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{3})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -16x-\frac{16}{3}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-112} & = & \color{red}{-147x} +24 \\\Leftrightarrow & -336x \color{red}{-112} \color{blue}{+112} \color{blue}{+147x} & = & \color{red}{-147x} +24 \color{blue}{+147x} \color{blue}{+112} \\\Leftrightarrow & -336x+147x& = & 24+112 \\\Leftrightarrow & \color{red}{-189} x& = & 136 \\\Leftrightarrow & x = \frac{136}{-189} & & \\\Leftrightarrow & x = \frac{-136}{189} & & \\ & V = \left\{ \frac{-136}{189} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & 8x+\frac{8}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & 8x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{440}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{440x} +40 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{-440x} & = & \color{red}{440x} +40 \color{blue}{-440x} \color{blue}{-66} \\\Leftrightarrow & -825x-440x& = & 40-66 \\\Leftrightarrow & \color{red}{-1265} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1265} & & \\\Leftrightarrow & x = \frac{26}{1265} & & \\ & V = \left\{ \frac{26}{1265} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{5}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -16x+\frac{20}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+60} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -336x \color{red}{+60} \color{blue}{-60} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-60} \\\Leftrightarrow & -336x+147x& = & 56-60 \\\Leftrightarrow & \color{red}{-189} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-189} & & \\\Leftrightarrow & x = \frac{4}{189} & & \\ & V = \left\{ \frac{4}{189} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{11})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{8}{11}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{-16} & = & \color{red}{110x} +77 \\\Leftrightarrow & -264x \color{red}{-16} \color{blue}{+16} \color{blue}{-110x} & = & \color{red}{110x} +77 \color{blue}{-110x} \color{blue}{+16} \\\Leftrightarrow & -264x-110x& = & 77+16 \\\Leftrightarrow & \color{red}{-374} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-374} & & \\\Leftrightarrow & x = \frac{-93}{374} & & \\ & V = \left\{ \frac{-93}{374} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{11})& = & -7x+\frac{7}{11} \\\Leftrightarrow & -16x+\frac{16}{11}& = & -7x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+16} & = & \color{red}{-77x} +7 \\\Leftrightarrow & -176x \color{red}{+16} \color{blue}{-16} \color{blue}{+77x} & = & \color{red}{-77x} +7 \color{blue}{+77x} \color{blue}{-16} \\\Leftrightarrow & -176x+77x& = & 7-16 \\\Leftrightarrow & \color{red}{-99} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-99} & & \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{3}{2})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{15}{2}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{+105} & = & \color{red}{98x} +20 \\\Leftrightarrow & -140x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +20 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & -140x-98x& = & 20-105 \\\Leftrightarrow & \color{red}{-238} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-238} & & \\\Leftrightarrow & x = \frac{5}{14} & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{3})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -10x-\frac{10}{3}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{40}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{-84x} +15 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{+84x} & = & \color{red}{-84x} +15 \color{blue}{+84x} \color{blue}{+40} \\\Leftrightarrow & -120x+84x& = & 15+40 \\\Leftrightarrow & \color{red}{-36} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-36} & & \\\Leftrightarrow & x = \frac{-55}{36} & & \\ & V = \left\{ \frac{-55}{36} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{3})& = & 7x+\frac{3}{8} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-384}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -384x \color{red}{-160} & = & \color{red}{168x} +9 \\\Leftrightarrow & -384x \color{red}{-160} \color{blue}{+160} \color{blue}{-168x} & = & \color{red}{168x} +9 \color{blue}{-168x} \color{blue}{+160} \\\Leftrightarrow & -384x-168x& = & 9+160 \\\Leftrightarrow & \color{red}{-552} x& = & 169 \\\Leftrightarrow & x = \frac{169}{-552} & & \\\Leftrightarrow & x = \frac{-169}{552} & & \\ & V = \left\{ \frac{-169}{552} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -4x+\frac{7}{2} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -4x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-40}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-24} & = & \color{red}{-40x} +35 \\\Leftrightarrow & 150x \color{red}{-24} \color{blue}{+24} \color{blue}{+40x} & = & \color{red}{-40x} +35 \color{blue}{+40x} \color{blue}{+24} \\\Leftrightarrow & 150x+40x& = & 35+24 \\\Leftrightarrow & \color{red}{190} x& = & 59 \\\Leftrightarrow & x = \frac{59}{190} & & \\ & V = \left\{ \frac{59}{190} \right\} & \\\end{align}\)
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