Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{1}{3})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -21x-\frac{7}{3}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{7}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-7} & = & \color{red}{24x} +2 \\\Leftrightarrow & -63x \color{red}{-7} \color{blue}{+7} \color{blue}{-24x} & = & \color{red}{24x} +2 \color{blue}{-24x} \color{blue}{+7} \\\Leftrightarrow & -63x-24x& = & 2+7 \\\Leftrightarrow & \color{red}{-87} x& = & 9 \\\Leftrightarrow & x = \frac{9}{-87} & & \\\Leftrightarrow & x = \frac{-3}{29} & & \\ & V = \left\{ \frac{-3}{29} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{3})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{8}{3}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{88}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-88} & = & \color{red}{231x} +18 \\\Leftrightarrow & 660x \color{red}{-88} \color{blue}{+88} \color{blue}{-231x} & = & \color{red}{231x} +18 \color{blue}{-231x} \color{blue}{+88} \\\Leftrightarrow & 660x-231x& = & 18+88 \\\Leftrightarrow & \color{red}{429} x& = & 106 \\\Leftrightarrow & x = \frac{106}{429} & & \\ & V = \left\{ \frac{106}{429} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{5}{3})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{+140} & = & \color{red}{147x} +12 \\\Leftrightarrow & -420x \color{red}{+140} \color{blue}{-140} \color{blue}{-147x} & = & \color{red}{147x} +12 \color{blue}{-147x} \color{blue}{-140} \\\Leftrightarrow & -420x-147x& = & 12-140 \\\Leftrightarrow & \color{red}{-567} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{-567} & & \\\Leftrightarrow & x = \frac{128}{567} & & \\ & V = \left\{ \frac{128}{567} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{5})& = & 6x+\frac{10}{11} \\\Leftrightarrow & -35x-\frac{14}{5}& = & 6x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1925}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{330}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1925x \color{red}{-154} & = & \color{red}{330x} +50 \\\Leftrightarrow & -1925x \color{red}{-154} \color{blue}{+154} \color{blue}{-330x} & = & \color{red}{330x} +50 \color{blue}{-330x} \color{blue}{+154} \\\Leftrightarrow & -1925x-330x& = & 50+154 \\\Leftrightarrow & \color{red}{-2255} x& = & 204 \\\Leftrightarrow & x = \frac{204}{-2255} & & \\\Leftrightarrow & x = \frac{-204}{2255} & & \\ & V = \left\{ \frac{-204}{2255} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 8x+\frac{7}{2} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 8x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{64x} +28 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-64x} & = & \color{red}{64x} +28 \color{blue}{-64x} \color{blue}{+21} \\\Leftrightarrow & 168x-64x& = & 28+21 \\\Leftrightarrow & \color{red}{104} x& = & 49 \\\Leftrightarrow & x = \frac{49}{104} & & \\ & V = \left\{ \frac{49}{104} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{2}{3})& = & -8x+\frac{9}{10} \\\Leftrightarrow & 35x+\frac{14}{3}& = & -8x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{1050}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{-240}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 1050x \color{red}{+140} & = & \color{red}{-240x} +27 \\\Leftrightarrow & 1050x \color{red}{+140} \color{blue}{-140} \color{blue}{+240x} & = & \color{red}{-240x} +27 \color{blue}{+240x} \color{blue}{-140} \\\Leftrightarrow & 1050x+240x& = & 27-140 \\\Leftrightarrow & \color{red}{1290} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{1290} & & \\ & V = \left\{ \frac{-113}{1290} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 4x-\frac{6}{7}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{-12} & = & \color{red}{42x} +49 \\\Leftrightarrow & 56x \color{red}{-12} \color{blue}{+12} \color{blue}{-42x} & = & \color{red}{42x} +49 \color{blue}{-42x} \color{blue}{+12} \\\Leftrightarrow & 56x-42x& = & 49+12 \\\Leftrightarrow & \color{red}{14} x& = & 61 \\\Leftrightarrow & x = \frac{61}{14} & & \\ & V = \left\{ \frac{61}{14} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{4}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x-\frac{16}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{176}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-176} & = & \color{red}{-275x} +30 \\\Leftrightarrow & -660x \color{red}{-176} \color{blue}{+176} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+176} \\\Leftrightarrow & -660x+275x& = & 30+176 \\\Leftrightarrow & \color{red}{-385} x& = & 206 \\\Leftrightarrow & x = \frac{206}{-385} & & \\\Leftrightarrow & x = \frac{-206}{385} & & \\ & V = \left\{ \frac{-206}{385} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{14}{3}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-42}{ \color{blue}{3} }x+ \frac{14}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -42x \color{red}{+14} & = & \color{red}{-9x} +10 \\\Leftrightarrow & -42x \color{red}{+14} \color{blue}{-14} \color{blue}{+9x} & = & \color{red}{-9x} +10 \color{blue}{+9x} \color{blue}{-14} \\\Leftrightarrow & -42x+9x& = & 10-14 \\\Leftrightarrow & \color{red}{-33} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-33} & & \\\Leftrightarrow & x = \frac{4}{33} & & \\ & V = \left\{ \frac{4}{33} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{9})& = & -6x+\frac{7}{10} \\\Leftrightarrow & -28x+\frac{28}{9}& = & -6x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-2520}{ \color{blue}{90} }x+ \frac{280}{ \color{blue}{90} })& = & (\frac{-540}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -2520x \color{red}{+280} & = & \color{red}{-540x} +63 \\\Leftrightarrow & -2520x \color{red}{+280} \color{blue}{-280} \color{blue}{+540x} & = & \color{red}{-540x} +63 \color{blue}{+540x} \color{blue}{-280} \\\Leftrightarrow & -2520x+540x& = & 63-280 \\\Leftrightarrow & \color{red}{-1980} x& = & -217 \\\Leftrightarrow & x = \frac{-217}{-1980} & & \\\Leftrightarrow & x = \frac{217}{1980} & & \\ & V = \left\{ \frac{217}{1980} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{4}{9} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{+162} & = & \color{red}{495x} +44 \\\Leftrightarrow & -1188x \color{red}{+162} \color{blue}{-162} \color{blue}{-495x} & = & \color{red}{495x} +44 \color{blue}{-495x} \color{blue}{-162} \\\Leftrightarrow & -1188x-495x& = & 44-162 \\\Leftrightarrow & \color{red}{-1683} x& = & -118 \\\Leftrightarrow & x = \frac{-118}{-1683} & & \\\Leftrightarrow & x = \frac{118}{1683} & & \\ & V = \left\{ \frac{118}{1683} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{7})& = & -4x+\frac{4}{9} \\\Leftrightarrow & 15x-\frac{25}{7}& = & -4x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{225}{ \color{blue}{63} })& = & (\frac{-252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-225} & = & \color{red}{-252x} +28 \\\Leftrightarrow & 945x \color{red}{-225} \color{blue}{+225} \color{blue}{+252x} & = & \color{red}{-252x} +28 \color{blue}{+252x} \color{blue}{+225} \\\Leftrightarrow & 945x+252x& = & 28+225 \\\Leftrightarrow & \color{red}{1197} x& = & 253 \\\Leftrightarrow & x = \frac{253}{1197} & & \\ & V = \left\{ \frac{253}{1197} \right\} & \\\end{align}\)
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