Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{105x} +25 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{+36} \\\Leftrightarrow & -450x-105x& = & 25+36 \\\Leftrightarrow & \color{red}{-555} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-555} & & \\\Leftrightarrow & x = \frac{-61}{555} & & \\ & V = \left\{ \frac{-61}{555} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & -8x+\frac{6}{7} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1176x \color{red}{+147} & = & \color{red}{-448x} +48 \\\Leftrightarrow & -1176x \color{red}{+147} \color{blue}{-147} \color{blue}{+448x} & = & \color{red}{-448x} +48 \color{blue}{+448x} \color{blue}{-147} \\\Leftrightarrow & -1176x+448x& = & 48-147 \\\Leftrightarrow & \color{red}{-728} x& = & -99 \\\Leftrightarrow & x = \frac{-99}{-728} & & \\\Leftrightarrow & x = \frac{99}{728} & & \\ & V = \left\{ \frac{99}{728} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & -7x+\frac{2}{5} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{14}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{+30} & = & \color{red}{-245x} +14 \\\Leftrightarrow & -210x \color{red}{+30} \color{blue}{-30} \color{blue}{+245x} & = & \color{red}{-245x} +14 \color{blue}{+245x} \color{blue}{-30} \\\Leftrightarrow & -210x+245x& = & 14-30 \\\Leftrightarrow & \color{red}{35} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{35} & & \\ & V = \left\{ \frac{-16}{35} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{2})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -28x-\frac{21}{2}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{231}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-231} & = & \color{red}{-110x} +10 \\\Leftrightarrow & -616x \color{red}{-231} \color{blue}{+231} \color{blue}{+110x} & = & \color{red}{-110x} +10 \color{blue}{+110x} \color{blue}{+231} \\\Leftrightarrow & -616x+110x& = & 10+231 \\\Leftrightarrow & \color{red}{-506} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-506} & & \\\Leftrightarrow & x = \frac{-241}{506} & & \\ & V = \left\{ \frac{-241}{506} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+165} & = & \color{red}{308x} +8 \\\Leftrightarrow & -264x \color{red}{+165} \color{blue}{-165} \color{blue}{-308x} & = & \color{red}{308x} +8 \color{blue}{-308x} \color{blue}{-165} \\\Leftrightarrow & -264x-308x& = & 8-165 \\\Leftrightarrow & \color{red}{-572} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-572} & & \\\Leftrightarrow & x = \frac{157}{572} & & \\ & V = \left\{ \frac{157}{572} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+54} & = & \color{red}{-165x} +22 \\\Leftrightarrow & -792x \color{red}{+54} \color{blue}{-54} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{-54} \\\Leftrightarrow & -792x+165x& = & 22-54 \\\Leftrightarrow & \color{red}{-627} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-627} & & \\\Leftrightarrow & x = \frac{32}{627} & & \\ & V = \left\{ \frac{32}{627} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{5}{7})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -12x+\frac{30}{7}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{+270} & = & \color{red}{-315x} +56 \\\Leftrightarrow & -756x \color{red}{+270} \color{blue}{-270} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-270} \\\Leftrightarrow & -756x+315x& = & 56-270 \\\Leftrightarrow & \color{red}{-441} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{-441} & & \\\Leftrightarrow & x = \frac{214}{441} & & \\ & V = \left\{ \frac{214}{441} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{3})& = & -9x+\frac{5}{12} \\\Leftrightarrow & -4x+\frac{8}{3}& = & -9x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-48}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -48x \color{red}{+32} & = & \color{red}{-108x} +5 \\\Leftrightarrow & -48x \color{red}{+32} \color{blue}{-32} \color{blue}{+108x} & = & \color{red}{-108x} +5 \color{blue}{+108x} \color{blue}{-32} \\\Leftrightarrow & -48x+108x& = & 5-32 \\\Leftrightarrow & \color{red}{60} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{60} & & \\\Leftrightarrow & x = \frac{-9}{20} & & \\ & V = \left\{ \frac{-9}{20} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x+ \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{+90} & = & \color{red}{-165x} +55 \\\Leftrightarrow & 594x \color{red}{+90} \color{blue}{-90} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{-90} \\\Leftrightarrow & 594x+165x& = & 55-90 \\\Leftrightarrow & \color{red}{759} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{759} & & \\ & V = \left\{ \frac{-35}{759} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{8})& = & -9x+\frac{8}{3} \\\Leftrightarrow & 28x+\frac{35}{8}& = & -9x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{105}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+105} & = & \color{red}{-216x} +64 \\\Leftrightarrow & 672x \color{red}{+105} \color{blue}{-105} \color{blue}{+216x} & = & \color{red}{-216x} +64 \color{blue}{+216x} \color{blue}{-105} \\\Leftrightarrow & 672x+216x& = & 64-105 \\\Leftrightarrow & \color{red}{888} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{888} & & \\ & V = \left\{ \frac{-41}{888} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{3})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{36}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+56} & = & \color{red}{36x} +9 \\\Leftrightarrow & 420x \color{red}{+56} \color{blue}{-56} \color{blue}{-36x} & = & \color{red}{36x} +9 \color{blue}{-36x} \color{blue}{-56} \\\Leftrightarrow & 420x-36x& = & 9-56 \\\Leftrightarrow & \color{red}{384} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{384} & & \\ & V = \left\{ \frac{-47}{384} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 8x-\frac{12}{11}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-36} & = & \color{red}{297x} +110 \\\Leftrightarrow & 264x \color{red}{-36} \color{blue}{+36} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{+36} \\\Leftrightarrow & 264x-297x& = & 110+36 \\\Leftrightarrow & \color{red}{-33} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-33} & & \\\Leftrightarrow & x = \frac{-146}{33} & & \\ & V = \left\{ \frac{-146}{33} \right\} & \\\end{align}\)
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