Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{3})& = & -8x+\frac{3}{2} \\\Leftrightarrow & 35x+\frac{28}{3}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{56}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+56} & = & \color{red}{-48x} +9 \\\Leftrightarrow & 210x \color{red}{+56} \color{blue}{-56} \color{blue}{+48x} & = & \color{red}{-48x} +9 \color{blue}{+48x} \color{blue}{-56} \\\Leftrightarrow & 210x+48x& = & 9-56 \\\Leftrightarrow & \color{red}{258} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{258} & & \\ & V = \left\{ \frac{-47}{258} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1650}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1650x \color{red}{-90} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1650x \color{red}{-90} \color{blue}{+90} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+90} \\\Leftrightarrow & -1650x+385x& = & 66+90 \\\Leftrightarrow & \color{red}{-1265} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-1265} & & \\\Leftrightarrow & x = \frac{-156}{1265} & & \\ & V = \left\{ \frac{-156}{1265} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{5}{4})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{15}{4}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{336}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-140}{ \color{blue}{28} }x+ \frac{32}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 336x \color{red}{-105} & = & \color{red}{-140x} +32 \\\Leftrightarrow & 336x \color{red}{-105} \color{blue}{+105} \color{blue}{+140x} & = & \color{red}{-140x} +32 \color{blue}{+140x} \color{blue}{+105} \\\Leftrightarrow & 336x+140x& = & 32+105 \\\Leftrightarrow & \color{red}{476} x& = & 137 \\\Leftrightarrow & x = \frac{137}{476} & & \\ & V = \left\{ \frac{137}{476} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{3}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{6}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-54} & = & \color{red}{-441x} +70 \\\Leftrightarrow & -378x \color{red}{-54} \color{blue}{+54} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+54} \\\Leftrightarrow & -378x+441x& = & 70+54 \\\Leftrightarrow & \color{red}{63} x& = & 124 \\\Leftrightarrow & x = \frac{124}{63} & & \\ & V = \left\{ \frac{124}{63} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{40}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-40} & = & \color{red}{-98x} +21 \\\Leftrightarrow & 280x \color{red}{-40} \color{blue}{+40} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{+40} \\\Leftrightarrow & 280x+98x& = & 21+40 \\\Leftrightarrow & \color{red}{378} x& = & 61 \\\Leftrightarrow & x = \frac{61}{378} & & \\ & V = \left\{ \frac{61}{378} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{7})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 8x+\frac{16}{7}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{448}{ \color{blue}{56} }x+ \frac{128}{ \color{blue}{56} })& = & (\frac{504}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 448x \color{red}{+128} & = & \color{red}{504x} +49 \\\Leftrightarrow & 448x \color{red}{+128} \color{blue}{-128} \color{blue}{-504x} & = & \color{red}{504x} +49 \color{blue}{-504x} \color{blue}{-128} \\\Leftrightarrow & 448x-504x& = & 49-128 \\\Leftrightarrow & \color{red}{-56} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-56} & & \\\Leftrightarrow & x = \frac{79}{56} & & \\ & V = \left\{ \frac{79}{56} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{12}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-84} & = & \color{red}{539x} +110 \\\Leftrightarrow & -1232x \color{red}{-84} \color{blue}{+84} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+84} \\\Leftrightarrow & -1232x-539x& = & 110+84 \\\Leftrightarrow & \color{red}{-1771} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-1771} & & \\\Leftrightarrow & x = \frac{-194}{1771} & & \\ & V = \left\{ \frac{-194}{1771} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -2x+\frac{9}{4} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{9}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{-8}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{-15} & = & \color{red}{-8x} +9 \\\Leftrightarrow & 60x \color{red}{-15} \color{blue}{+15} \color{blue}{+8x} & = & \color{red}{-8x} +9 \color{blue}{+8x} \color{blue}{+15} \\\Leftrightarrow & 60x+8x& = & 9+15 \\\Leftrightarrow & \color{red}{68} x& = & 24 \\\Leftrightarrow & x = \frac{24}{68} & & \\\Leftrightarrow & x = \frac{6}{17} & & \\ & V = \left\{ \frac{6}{17} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{7}{2} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x+ \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{+60} & = & \color{red}{-70x} +49 \\\Leftrightarrow & -168x \color{red}{+60} \color{blue}{-60} \color{blue}{+70x} & = & \color{red}{-70x} +49 \color{blue}{+70x} \color{blue}{-60} \\\Leftrightarrow & -168x+70x& = & 49-60 \\\Leftrightarrow & \color{red}{-98} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-98} & & \\\Leftrightarrow & x = \frac{11}{98} & & \\ & V = \left\{ \frac{11}{98} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{11})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{10}{11}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-264}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} })& = & (\frac{594}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -264x \color{red}{+60} & = & \color{red}{594x} +55 \\\Leftrightarrow & -264x \color{red}{+60} \color{blue}{-60} \color{blue}{-594x} & = & \color{red}{594x} +55 \color{blue}{-594x} \color{blue}{-60} \\\Leftrightarrow & -264x-594x& = & 55-60 \\\Leftrightarrow & \color{red}{-858} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-858} & & \\\Leftrightarrow & x = \frac{5}{858} & & \\ & V = \left\{ \frac{5}{858} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-60} \\\Leftrightarrow & 336x+63x& = & 14-60 \\\Leftrightarrow & \color{red}{399} x& = & -46 \\\Leftrightarrow & x = \frac{-46}{399} & & \\ & V = \left\{ \frac{-46}{399} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+220} & = & \color{red}{231x} +42 \\\Leftrightarrow & 1540x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & 1540x-231x& = & 42-220 \\\Leftrightarrow & \color{red}{1309} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{1309} & & \\ & V = \left\{ \frac{-178}{1309} \right\} & \\\end{align}\)
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