Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{6})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{35}{6}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{210}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 210x \color{red}{+35} & = & \color{red}{18x} +16 \\\Leftrightarrow & 210x \color{red}{+35} \color{blue}{-35} \color{blue}{-18x} & = & \color{red}{18x} +16 \color{blue}{-18x} \color{blue}{-35} \\\Leftrightarrow & 210x-18x& = & 16-35 \\\Leftrightarrow & \color{red}{192} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{192} & & \\ & V = \left\{ \frac{-19}{192} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{4}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+4} & = & \color{red}{45x} +6 \\\Leftrightarrow & 54x \color{red}{+4} \color{blue}{-4} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-4} \\\Leftrightarrow & 54x-45x& = & 6-4 \\\Leftrightarrow & \color{red}{9} x& = & 2 \\\Leftrightarrow & x = \frac{2}{9} & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{5})& = & -3x+\frac{10}{3} \\\Leftrightarrow & -8x-\frac{4}{5}& = & -3x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-12} & = & \color{red}{-45x} +50 \\\Leftrightarrow & -120x \color{red}{-12} \color{blue}{+12} \color{blue}{+45x} & = & \color{red}{-45x} +50 \color{blue}{+45x} \color{blue}{+12} \\\Leftrightarrow & -120x+45x& = & 50+12 \\\Leftrightarrow & \color{red}{-75} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-75} & & \\\Leftrightarrow & x = \frac{-62}{75} & & \\ & V = \left\{ \frac{-62}{75} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x-\frac{6}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-60}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{70x} +25 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+12} \\\Leftrightarrow & -60x-70x& = & 25+12 \\\Leftrightarrow & \color{red}{-130} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-130} & & \\\Leftrightarrow & x = \frac{-37}{130} & & \\ & V = \left\{ \frac{-37}{130} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+24} & = & \color{red}{70x} +25 \\\Leftrightarrow & 60x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & 60x-70x& = & 25-24 \\\Leftrightarrow & \color{red}{-10} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-10} & & \\\Leftrightarrow & x = \frac{-1}{10} & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 7x+\frac{7}{2} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{224}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 224x \color{red}{+40} & = & \color{red}{98x} +49 \\\Leftrightarrow & 224x \color{red}{+40} \color{blue}{-40} \color{blue}{-98x} & = & \color{red}{98x} +49 \color{blue}{-98x} \color{blue}{-40} \\\Leftrightarrow & 224x-98x& = & 49-40 \\\Leftrightarrow & \color{red}{126} x& = & 9 \\\Leftrightarrow & x = \frac{9}{126} & & \\\Leftrightarrow & x = \frac{1}{14} & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{8})& = & -5x+\frac{6}{5} \\\Leftrightarrow & -12x-\frac{15}{8}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-480}{ \color{blue}{40} }x- \frac{75}{ \color{blue}{40} })& = & (\frac{-200}{ \color{blue}{40} }x+ \frac{48}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -480x \color{red}{-75} & = & \color{red}{-200x} +48 \\\Leftrightarrow & -480x \color{red}{-75} \color{blue}{+75} \color{blue}{+200x} & = & \color{red}{-200x} +48 \color{blue}{+200x} \color{blue}{+75} \\\Leftrightarrow & -480x+200x& = & 48+75 \\\Leftrightarrow & \color{red}{-280} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-280} & & \\\Leftrightarrow & x = \frac{-123}{280} & & \\ & V = \left\{ \frac{-123}{280} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -2x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -2x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{120}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 120x \color{red}{+15} & = & \color{red}{-16x} +28 \\\Leftrightarrow & 120x \color{red}{+15} \color{blue}{-15} \color{blue}{+16x} & = & \color{red}{-16x} +28 \color{blue}{+16x} \color{blue}{-15} \\\Leftrightarrow & 120x+16x& = & 28-15 \\\Leftrightarrow & \color{red}{136} x& = & 13 \\\Leftrightarrow & x = \frac{13}{136} & & \\ & V = \left\{ \frac{13}{136} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{5}{11})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x-\frac{10}{11}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{-30} & = & \color{red}{165x} +88 \\\Leftrightarrow & 198x \color{red}{-30} \color{blue}{+30} \color{blue}{-165x} & = & \color{red}{165x} +88 \color{blue}{-165x} \color{blue}{+30} \\\Leftrightarrow & 198x-165x& = & 88+30 \\\Leftrightarrow & \color{red}{33} x& = & 118 \\\Leftrightarrow & x = \frac{118}{33} & & \\ & V = \left\{ \frac{118}{33} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{9})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{10}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-10} & = & \color{red}{-63x} +6 \\\Leftrightarrow & -90x \color{red}{-10} \color{blue}{+10} \color{blue}{+63x} & = & \color{red}{-63x} +6 \color{blue}{+63x} \color{blue}{+10} \\\Leftrightarrow & -90x+63x& = & 6+10 \\\Leftrightarrow & \color{red}{-27} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-27} & & \\\Leftrightarrow & x = \frac{-16}{27} & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{9})& = & -5x+\frac{2}{5} \\\Leftrightarrow & -4x+\frac{8}{9}& = & -5x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{+40} & = & \color{red}{-225x} +18 \\\Leftrightarrow & -180x \color{red}{+40} \color{blue}{-40} \color{blue}{+225x} & = & \color{red}{-225x} +18 \color{blue}{+225x} \color{blue}{-40} \\\Leftrightarrow & -180x+225x& = & 18-40 \\\Leftrightarrow & \color{red}{45} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{45} & & \\ & V = \left\{ \frac{-22}{45} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{11})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{16}{11}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{144}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-144} & = & \color{red}{891x} +88 \\\Leftrightarrow & -1980x \color{red}{-144} \color{blue}{+144} \color{blue}{-891x} & = & \color{red}{891x} +88 \color{blue}{-891x} \color{blue}{+144} \\\Leftrightarrow & -1980x-891x& = & 88+144 \\\Leftrightarrow & \color{red}{-2871} x& = & 232 \\\Leftrightarrow & x = \frac{232}{-2871} & & \\\Leftrightarrow & x = \frac{-8}{99} & & \\ & V = \left\{ \frac{-8}{99} \right\} & \\\end{align}\)