Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{2}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{8}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x- \frac{8}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{-8} & = & \color{red}{21x} +4 \\\Leftrightarrow & -60x \color{red}{-8} \color{blue}{+8} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+8} \\\Leftrightarrow & -60x-21x& = & 4+8 \\\Leftrightarrow & \color{red}{-81} x& = & 12 \\\Leftrightarrow & x = \frac{12}{-81} & & \\\Leftrightarrow & x = \frac{-4}{27} & & \\ & V = \left\{ \frac{-4}{27} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{4}{11})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{12}{11}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{-12} & = & \color{red}{-77x} +6 \\\Leftrightarrow & -66x \color{red}{-12} \color{blue}{+12} \color{blue}{+77x} & = & \color{red}{-77x} +6 \color{blue}{+77x} \color{blue}{+12} \\\Leftrightarrow & -66x+77x& = & 6+12 \\\Leftrightarrow & \color{red}{11} x& = & 18 \\\Leftrightarrow & x = \frac{18}{11} & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{3})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -20x+\frac{16}{3}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x+ \frac{32}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{+32} & = & \color{red}{-42x} +7 \\\Leftrightarrow & -120x \color{red}{+32} \color{blue}{-32} \color{blue}{+42x} & = & \color{red}{-42x} +7 \color{blue}{+42x} \color{blue}{-32} \\\Leftrightarrow & -120x+42x& = & 7-32 \\\Leftrightarrow & \color{red}{-78} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-78} & & \\\Leftrightarrow & x = \frac{25}{78} & & \\ & V = \left\{ \frac{25}{78} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{7})& = & 7x+\frac{5}{11} \\\Leftrightarrow & -6x-\frac{8}{7}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{88}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-88} & = & \color{red}{539x} +35 \\\Leftrightarrow & -462x \color{red}{-88} \color{blue}{+88} \color{blue}{-539x} & = & \color{red}{539x} +35 \color{blue}{-539x} \color{blue}{+88} \\\Leftrightarrow & -462x-539x& = & 35+88 \\\Leftrightarrow & \color{red}{-1001} x& = & 123 \\\Leftrightarrow & x = \frac{123}{-1001} & & \\\Leftrightarrow & x = \frac{-123}{1001} & & \\ & V = \left\{ \frac{-123}{1001} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-60} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 420x \color{red}{-60} \color{blue}{+60} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+60} \\\Leftrightarrow & 420x+175x& = & 42+60 \\\Leftrightarrow & \color{red}{595} x& = & 102 \\\Leftrightarrow & x = \frac{102}{595} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x+\frac{8}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-224}{ \color{blue}{14} }x+ \frac{16}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -224x \color{red}{+16} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -224x \color{red}{+16} \color{blue}{-16} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-16} \\\Leftrightarrow & -224x+98x& = & 21-16 \\\Leftrightarrow & \color{red}{-126} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-126} & & \\\Leftrightarrow & x = \frac{-5}{126} & & \\ & V = \left\{ \frac{-5}{126} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{5}{3})& = & -3x+\frac{3}{11} \\\Leftrightarrow & -28x-\frac{35}{3}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{9}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-385} & = & \color{red}{-99x} +9 \\\Leftrightarrow & -924x \color{red}{-385} \color{blue}{+385} \color{blue}{+99x} & = & \color{red}{-99x} +9 \color{blue}{+99x} \color{blue}{+385} \\\Leftrightarrow & -924x+99x& = & 9+385 \\\Leftrightarrow & \color{red}{-825} x& = & 394 \\\Leftrightarrow & x = \frac{394}{-825} & & \\\Leftrightarrow & x = \frac{-394}{825} & & \\ & V = \left\{ \frac{-394}{825} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{2}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & -10x+\frac{4}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+28} & = & \color{red}{-245x} +45 \\\Leftrightarrow & -350x \color{red}{+28} \color{blue}{-28} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{-28} \\\Leftrightarrow & -350x+245x& = & 45-28 \\\Leftrightarrow & \color{red}{-105} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-105} & & \\\Leftrightarrow & x = \frac{-17}{105} & & \\ & V = \left\{ \frac{-17}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{27}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+56} & = & \color{red}{315x} +27 \\\Leftrightarrow & 504x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +27 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & 504x-315x& = & 27-56 \\\Leftrightarrow & \color{red}{189} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{189} & & \\ & V = \left\{ \frac{-29}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{9})& = & -8x+\frac{7}{10} \\\Leftrightarrow & 35x-\frac{35}{9}& = & -8x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{3150}{ \color{blue}{90} }x- \frac{350}{ \color{blue}{90} })& = & (\frac{-720}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 3150x \color{red}{-350} & = & \color{red}{-720x} +63 \\\Leftrightarrow & 3150x \color{red}{-350} \color{blue}{+350} \color{blue}{+720x} & = & \color{red}{-720x} +63 \color{blue}{+720x} \color{blue}{+350} \\\Leftrightarrow & 3150x+720x& = & 63+350 \\\Leftrightarrow & \color{red}{3870} x& = & 413 \\\Leftrightarrow & x = \frac{413}{3870} & & \\ & V = \left\{ \frac{413}{3870} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{264}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+264} & = & \color{red}{-495x} +25 \\\Leftrightarrow & -990x \color{red}{+264} \color{blue}{-264} \color{blue}{+495x} & = & \color{red}{-495x} +25 \color{blue}{+495x} \color{blue}{-264} \\\Leftrightarrow & -990x+495x& = & 25-264 \\\Leftrightarrow & \color{red}{-495} x& = & -239 \\\Leftrightarrow & x = \frac{-239}{-495} & & \\\Leftrightarrow & x = \frac{239}{495} & & \\ & V = \left\{ \frac{239}{495} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -3x+\frac{2}{3} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -3x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{+18} & = & \color{red}{-63x} +14 \\\Leftrightarrow & 84x \color{red}{+18} \color{blue}{-18} \color{blue}{+63x} & = & \color{red}{-63x} +14 \color{blue}{+63x} \color{blue}{-18} \\\Leftrightarrow & 84x+63x& = & 14-18 \\\Leftrightarrow & \color{red}{147} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{147} & & \\ & V = \left\{ \frac{-4}{147} \right\} & \\\end{align}\)