Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

  1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -3x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -3x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+6} & = & \color{red}{-21x} +10 \\\Leftrightarrow & 28x \color{red}{+6} \color{blue}{-6} \color{blue}{+21x} & = & \color{red}{-21x} +10 \color{blue}{+21x} \color{blue}{-6} \\\Leftrightarrow & 28x+21x& = & 10-6 \\\Leftrightarrow & \color{red}{49} x& = & 4 \\\Leftrightarrow & x = \frac{4}{49} & & \\ & V = \left\{ \frac{4}{49} \right\} & \\\end{align}\)
  2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -24x-\frac{24}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1680}{ \color{blue}{70} }x- \frac{240}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1680x \color{red}{-240} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -1680x \color{red}{-240} \color{blue}{+240} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{+240} \\\Leftrightarrow & -1680x+350x& = & 63+240 \\\Leftrightarrow & \color{red}{-1330} x& = & 303 \\\Leftrightarrow & x = \frac{303}{-1330} & & \\\Leftrightarrow & x = \frac{-303}{1330} & & \\ & V = \left\{ \frac{-303}{1330} \right\} & \\\end{align}\)
  3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{4}{5})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{735}{ \color{blue}{35} }x- \frac{196}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 735x \color{red}{-196} & = & \color{red}{-70x} +45 \\\Leftrightarrow & 735x \color{red}{-196} \color{blue}{+196} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+196} \\\Leftrightarrow & 735x+70x& = & 45+196 \\\Leftrightarrow & \color{red}{805} x& = & 241 \\\Leftrightarrow & x = \frac{241}{805} & & \\ & V = \left\{ \frac{241}{805} \right\} & \\\end{align}\)
  4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -4x+\frac{8}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-168}{ \color{blue}{42} }x+ \frac{48}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -168x \color{red}{+48} & = & \color{red}{378x} +35 \\\Leftrightarrow & -168x \color{red}{+48} \color{blue}{-48} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{-48} \\\Leftrightarrow & -168x-378x& = & 35-48 \\\Leftrightarrow & \color{red}{-546} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-546} & & \\\Leftrightarrow & x = \frac{1}{42} & & \\ & V = \left\{ \frac{1}{42} \right\} & \\\end{align}\)
  5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{3}{8})& = & -7x+\frac{9}{10} \\\Leftrightarrow & 20x-\frac{15}{8}& = & -7x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{800}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 800x \color{red}{-75} & = & \color{red}{-280x} +36 \\\Leftrightarrow & 800x \color{red}{-75} \color{blue}{+75} \color{blue}{+280x} & = & \color{red}{-280x} +36 \color{blue}{+280x} \color{blue}{+75} \\\Leftrightarrow & 800x+280x& = & 36+75 \\\Leftrightarrow & \color{red}{1080} x& = & 111 \\\Leftrightarrow & x = \frac{111}{1080} & & \\\Leftrightarrow & x = \frac{37}{360} & & \\ & V = \left\{ \frac{37}{360} \right\} & \\\end{align}\)
  6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{11})& = & -5x+\frac{5}{9} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2376}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{55}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2376x \color{red}{+162} & = & \color{red}{-495x} +55 \\\Leftrightarrow & -2376x \color{red}{+162} \color{blue}{-162} \color{blue}{+495x} & = & \color{red}{-495x} +55 \color{blue}{+495x} \color{blue}{-162} \\\Leftrightarrow & -2376x+495x& = & 55-162 \\\Leftrightarrow & \color{red}{-1881} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1881} & & \\\Leftrightarrow & x = \frac{107}{1881} & & \\ & V = \left\{ \frac{107}{1881} \right\} & \\\end{align}\)
  7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{5}{9})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{63x} +30 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & 180x-63x& = & 30-20 \\\Leftrightarrow & \color{red}{117} x& = & 10 \\\Leftrightarrow & x = \frac{10}{117} & & \\ & V = \left\{ \frac{10}{117} \right\} & \\\end{align}\)
  8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{3}{5})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 8x+\frac{12}{5}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{105x} +25 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +25 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 120x-105x& = & 25-36 \\\Leftrightarrow & \color{red}{15} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{15} & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
  9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{7})& = & 9x+\frac{2}{3} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+18} & = & \color{red}{189x} +14 \\\Leftrightarrow & -84x \color{red}{+18} \color{blue}{-18} \color{blue}{-189x} & = & \color{red}{189x} +14 \color{blue}{-189x} \color{blue}{-18} \\\Leftrightarrow & -84x-189x& = & 14-18 \\\Leftrightarrow & \color{red}{-273} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-273} & & \\\Leftrightarrow & x = \frac{4}{273} & & \\ & V = \left\{ \frac{4}{273} \right\} & \\\end{align}\)
  10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{7})& = & -2x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{20}{7}& = & -2x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-220} & = & \color{red}{-154x} +28 \\\Leftrightarrow & 1155x \color{red}{-220} \color{blue}{+220} \color{blue}{+154x} & = & \color{red}{-154x} +28 \color{blue}{+154x} \color{blue}{+220} \\\Leftrightarrow & 1155x+154x& = & 28+220 \\\Leftrightarrow & \color{red}{1309} x& = & 248 \\\Leftrightarrow & x = \frac{248}{1309} & & \\ & V = \left\{ \frac{248}{1309} \right\} & \\\end{align}\)
  11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{10}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-10} & = & \color{red}{-49x} +6 \\\Leftrightarrow & -70x \color{red}{-10} \color{blue}{+10} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{+10} \\\Leftrightarrow & -70x+49x& = & 6+10 \\\Leftrightarrow & \color{red}{-21} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-21} & & \\\Leftrightarrow & x = \frac{-16}{21} & & \\ & V = \left\{ \frac{-16}{21} \right\} & \\\end{align}\)
  12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{6})& = & 5x+\frac{9}{7} \\\Leftrightarrow & -28x+\frac{35}{6}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 6 en 7 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1176}{ \color{blue}{42} }x+ \frac{245}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{54}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1176x \color{red}{+245} & = & \color{red}{210x} +54 \\\Leftrightarrow & -1176x \color{red}{+245} \color{blue}{-245} \color{blue}{-210x} & = & \color{red}{210x} +54 \color{blue}{-210x} \color{blue}{-245} \\\Leftrightarrow & -1176x-210x& = & 54-245 \\\Leftrightarrow & \color{red}{-1386} x& = & -191 \\\Leftrightarrow & x = \frac{-191}{-1386} & & \\\Leftrightarrow & x = \frac{191}{1386} & & \\ & V = \left\{ \frac{191}{1386} \right\} & \\\end{align}\)
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