Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -18x-\frac{12}{5}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-132} & = & \color{red}{-495x} +25 \\\Leftrightarrow & -990x \color{red}{-132} \color{blue}{+132} \color{blue}{+495x} & = & \color{red}{-495x} +25 \color{blue}{+495x} \color{blue}{+132} \\\Leftrightarrow & -990x+495x& = & 25+132 \\\Leftrightarrow & \color{red}{-495} x& = & 157 \\\Leftrightarrow & x = \frac{157}{-495} & & \\\Leftrightarrow & x = \frac{-157}{495} & & \\ & V = \left\{ \frac{-157}{495} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x+\frac{2}{5})& = & 5x+\frac{5}{2} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{180}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 180x \color{red}{-24} & = & \color{red}{50x} +25 \\\Leftrightarrow & 180x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +25 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 180x-50x& = & 25+24 \\\Leftrightarrow & \color{red}{130} x& = & 49 \\\Leftrightarrow & x = \frac{49}{130} & & \\ & V = \left\{ \frac{49}{130} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{90}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 90x \color{red}{+36} & = & \color{red}{-75x} +40 \\\Leftrightarrow & 90x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 90x+75x& = & 40-36 \\\Leftrightarrow & \color{red}{165} x& = & 4 \\\Leftrightarrow & x = \frac{4}{165} & & \\ & V = \left\{ \frac{4}{165} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{6})& = & 5x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{6}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x- \frac{175}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{36}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{-175} & = & \color{red}{150x} +36 \\\Leftrightarrow & 420x \color{red}{-175} \color{blue}{+175} \color{blue}{-150x} & = & \color{red}{150x} +36 \color{blue}{-150x} \color{blue}{+175} \\\Leftrightarrow & 420x-150x& = & 36+175 \\\Leftrightarrow & \color{red}{270} x& = & 211 \\\Leftrightarrow & x = \frac{211}{270} & & \\ & V = \left\{ \frac{211}{270} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{4}{11})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{385x} +33 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{-385x} & = & \color{red}{385x} +33 \color{blue}{-385x} \color{blue}{+84} \\\Leftrightarrow & 924x-385x& = & 33+84 \\\Leftrightarrow & \color{red}{539} x& = & 117 \\\Leftrightarrow & x = \frac{117}{539} & & \\ & V = \left\{ \frac{117}{539} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{9})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{-891x} +54 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{+891x} & = & \color{red}{-891x} +54 \color{blue}{+891x} \color{blue}{-88} \\\Leftrightarrow & -792x+891x& = & 54-88 \\\Leftrightarrow & \color{red}{99} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{99} & & \\ & V = \left\{ \frac{-34}{99} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 30x-\frac{30}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+90} \\\Leftrightarrow & 990x+231x& = & 88+90 \\\Leftrightarrow & \color{red}{1221} x& = & 178 \\\Leftrightarrow & x = \frac{178}{1221} & & \\ & V = \left\{ \frac{178}{1221} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -16x+\frac{8}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-176}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -176x \color{red}{+8} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -176x \color{red}{+8} \color{blue}{-8} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{-8} \\\Leftrightarrow & -176x+77x& = & 6-8 \\\Leftrightarrow & \color{red}{-99} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-99} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{3})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 12x+\frac{20}{3}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+140} & = & \color{red}{-105x} +6 \\\Leftrightarrow & 252x \color{red}{+140} \color{blue}{-140} \color{blue}{+105x} & = & \color{red}{-105x} +6 \color{blue}{+105x} \color{blue}{-140} \\\Leftrightarrow & 252x+105x& = & 6-140 \\\Leftrightarrow & \color{red}{357} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{357} & & \\ & V = \left\{ \frac{-134}{357} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{4}{5})& = & 7x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{24}{5}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-264} & = & \color{red}{385x} +10 \\\Leftrightarrow & 660x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +10 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 660x-385x& = & 10+264 \\\Leftrightarrow & \color{red}{275} x& = & 274 \\\Leftrightarrow & x = \frac{274}{275} & & \\ & V = \left\{ \frac{274}{275} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{11})& = & -8x+\frac{4}{5} \\\Leftrightarrow & -21x+\frac{28}{11}& = & -8x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1155}{ \color{blue}{55} }x+ \frac{140}{ \color{blue}{55} })& = & (\frac{-440}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1155x \color{red}{+140} & = & \color{red}{-440x} +44 \\\Leftrightarrow & -1155x \color{red}{+140} \color{blue}{-140} \color{blue}{+440x} & = & \color{red}{-440x} +44 \color{blue}{+440x} \color{blue}{-140} \\\Leftrightarrow & -1155x+440x& = & 44-140 \\\Leftrightarrow & \color{red}{-715} x& = & -96 \\\Leftrightarrow & x = \frac{-96}{-715} & & \\\Leftrightarrow & x = \frac{96}{715} & & \\ & V = \left\{ \frac{96}{715} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -9x-\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -315x \color{red}{-84} & = & \color{red}{175x} +20 \\\Leftrightarrow & -315x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & -315x-175x& = & 20+84 \\\Leftrightarrow & \color{red}{-490} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-490} & & \\\Leftrightarrow & x = \frac{-52}{245} & & \\ & V = \left\{ \frac{-52}{245} \right\} & \\\end{align}\)
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