Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 24x-\frac{24}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{840}{ \color{blue}{35} }x- \frac{120}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 840x \color{red}{-120} & = & \color{red}{175x} +42 \\\Leftrightarrow & 840x \color{red}{-120} \color{blue}{+120} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{+120} \\\Leftrightarrow & 840x-175x& = & 42+120 \\\Leftrightarrow & \color{red}{665} x& = & 162 \\\Leftrightarrow & x = \frac{162}{665} & & \\ & V = \left\{ \frac{162}{665} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 7x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 7x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{42}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{42x} +27 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-42x} & = & \color{red}{42x} +27 \color{blue}{-42x} \color{blue}{+40} \\\Leftrightarrow & -120x-42x& = & 27+40 \\\Leftrightarrow & \color{red}{-162} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-162} & & \\\Leftrightarrow & x = \frac{-67}{162} & & \\ & V = \left\{ \frac{-67}{162} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{4}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -16x-\frac{16}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{-48} & = & \color{red}{147x} +70 \\\Leftrightarrow & -336x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & -336x-147x& = & 70+48 \\\Leftrightarrow & \color{red}{-483} x& = & 118 \\\Leftrightarrow & x = \frac{118}{-483} & & \\\Leftrightarrow & x = \frac{-118}{483} & & \\ & V = \left\{ \frac{-118}{483} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -4x+\frac{10}{7}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-280}{ \color{blue}{70} }x+ \frac{100}{ \color{blue}{70} })& = & (\frac{350}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -280x \color{red}{+100} & = & \color{red}{350x} +21 \\\Leftrightarrow & -280x \color{red}{+100} \color{blue}{-100} \color{blue}{-350x} & = & \color{red}{350x} +21 \color{blue}{-350x} \color{blue}{-100} \\\Leftrightarrow & -280x-350x& = & 21-100 \\\Leftrightarrow & \color{red}{-630} x& = & -79 \\\Leftrightarrow & x = \frac{-79}{-630} & & \\\Leftrightarrow & x = \frac{79}{630} & & \\ & V = \left\{ \frac{79}{630} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+270} & = & \color{red}{315x} +28 \\\Leftrightarrow & -756x \color{red}{+270} \color{blue}{-270} \color{blue}{-315x} & = & \color{red}{315x} +28 \color{blue}{-315x} \color{blue}{-270} \\\Leftrightarrow & -756x-315x& = & 28-270 \\\Leftrightarrow & \color{red}{-1071} x& = & -242 \\\Leftrightarrow & x = \frac{-242}{-1071} & & \\\Leftrightarrow & x = \frac{242}{1071} & & \\ & V = \left\{ \frac{242}{1071} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x-\frac{4}{11})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 6x-\frac{12}{11}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{-84} & = & \color{red}{539x} +110 \\\Leftrightarrow & 462x \color{red}{-84} \color{blue}{+84} \color{blue}{-539x} & = & \color{red}{539x} +110 \color{blue}{-539x} \color{blue}{+84} \\\Leftrightarrow & 462x-539x& = & 110+84 \\\Leftrightarrow & \color{red}{-77} x& = & 194 \\\Leftrightarrow & x = \frac{194}{-77} & & \\\Leftrightarrow & x = \frac{-194}{77} & & \\ & V = \left\{ \frac{-194}{77} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{7})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x+\frac{25}{7}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{275}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+275} & = & \color{red}{539x} +14 \\\Leftrightarrow & -770x \color{red}{+275} \color{blue}{-275} \color{blue}{-539x} & = & \color{red}{539x} +14 \color{blue}{-539x} \color{blue}{-275} \\\Leftrightarrow & -770x-539x& = & 14-275 \\\Leftrightarrow & \color{red}{-1309} x& = & -261 \\\Leftrightarrow & x = \frac{-261}{-1309} & & \\\Leftrightarrow & x = \frac{261}{1309} & & \\ & V = \left\{ \frac{261}{1309} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{4}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{8}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{40}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-40} & = & \color{red}{-385x} +66 \\\Leftrightarrow & 440x \color{red}{-40} \color{blue}{+40} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+40} \\\Leftrightarrow & 440x+385x& = & 66+40 \\\Leftrightarrow & \color{red}{825} x& = & 106 \\\Leftrightarrow & x = \frac{106}{825} & & \\ & V = \left\{ \frac{106}{825} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -28x+\frac{35}{3}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x+ \frac{175}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{+175} & = & \color{red}{-75x} +6 \\\Leftrightarrow & -420x \color{red}{+175} \color{blue}{-175} \color{blue}{+75x} & = & \color{red}{-75x} +6 \color{blue}{+75x} \color{blue}{-175} \\\Leftrightarrow & -420x+75x& = & 6-175 \\\Leftrightarrow & \color{red}{-345} x& = & -169 \\\Leftrightarrow & x = \frac{-169}{-345} & & \\\Leftrightarrow & x = \frac{169}{345} & & \\ & V = \left\{ \frac{169}{345} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -990x \color{red}{+54} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -990x \color{red}{+54} \color{blue}{-54} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-54} \\\Leftrightarrow & -990x+231x& = & 88-54 \\\Leftrightarrow & \color{red}{-759} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-759} & & \\\Leftrightarrow & x = \frac{-34}{759} & & \\ & V = \left\{ \frac{-34}{759} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{2}{7})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -6x-\frac{4}{7}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-378}{ \color{blue}{63} }x- \frac{36}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -378x \color{red}{-36} & = & \color{red}{-441x} +70 \\\Leftrightarrow & -378x \color{red}{-36} \color{blue}{+36} \color{blue}{+441x} & = & \color{red}{-441x} +70 \color{blue}{+441x} \color{blue}{+36} \\\Leftrightarrow & -378x+441x& = & 70+36 \\\Leftrightarrow & \color{red}{63} x& = & 106 \\\Leftrightarrow & x = \frac{106}{63} & & \\ & V = \left\{ \frac{106}{63} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+2)& = & 8x+\frac{8}{9} \\\Leftrightarrow & -21x-14& = & 8x+\frac{8}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{126}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-126} & = & \color{red}{72x} +8 \\\Leftrightarrow & -189x \color{red}{-126} \color{blue}{+126} \color{blue}{-72x} & = & \color{red}{72x} +8 \color{blue}{-72x} \color{blue}{+126} \\\Leftrightarrow & -189x-72x& = & 8+126 \\\Leftrightarrow & \color{red}{-261} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-261} & & \\\Leftrightarrow & x = \frac{-134}{261} & & \\ & V = \left\{ \frac{-134}{261} \right\} & \\\end{align}\)
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