Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{11})& = & 8x+\frac{2}{3} \\\Leftrightarrow & 35x+\frac{35}{11}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{264}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{264x} +22 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-264x} & = & \color{red}{264x} +22 \color{blue}{-264x} \color{blue}{-105} \\\Leftrightarrow & 1155x-264x& = & 22-105 \\\Leftrightarrow & \color{red}{891} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{891} & & \\ & V = \left\{ \frac{-83}{891} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{6}{11}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{12}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+12} & = & \color{red}{-110x} +55 \\\Leftrightarrow & -264x \color{red}{+12} \color{blue}{-12} \color{blue}{+110x} & = & \color{red}{-110x} +55 \color{blue}{+110x} \color{blue}{-12} \\\Leftrightarrow & -264x+110x& = & 55-12 \\\Leftrightarrow & \color{red}{-154} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-154} & & \\\Leftrightarrow & x = \frac{-43}{154} & & \\ & V = \left\{ \frac{-43}{154} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{+12} & = & \color{red}{45x} +20 \\\Leftrightarrow & 150x \color{red}{+12} \color{blue}{-12} \color{blue}{-45x} & = & \color{red}{45x} +20 \color{blue}{-45x} \color{blue}{-12} \\\Leftrightarrow & 150x-45x& = & 20-12 \\\Leftrightarrow & \color{red}{105} x& = & 8 \\\Leftrightarrow & x = \frac{8}{105} & & \\ & V = \left\{ \frac{8}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{9})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{10}{9}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-110} & = & \color{red}{-693x} +54 \\\Leftrightarrow & -990x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +54 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & -990x+693x& = & 54+110 \\\Leftrightarrow & \color{red}{-297} x& = & 164 \\\Leftrightarrow & x = \frac{164}{-297} & & \\\Leftrightarrow & x = \frac{-164}{297} & & \\ & V = \left\{ \frac{-164}{297} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{7})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 18x-\frac{12}{7}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{-132} & = & \color{red}{-385x} +14 \\\Leftrightarrow & 1386x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +14 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 1386x+385x& = & 14+132 \\\Leftrightarrow & \color{red}{1771} x& = & 146 \\\Leftrightarrow & x = \frac{146}{1771} & & \\ & V = \left\{ \frac{146}{1771} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -16x-\frac{12}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{-12} & = & \color{red}{-49x} +10 \\\Leftrightarrow & -112x \color{red}{-12} \color{blue}{+12} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{+12} \\\Leftrightarrow & -112x+49x& = & 10+12 \\\Leftrightarrow & \color{red}{-63} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-63} & & \\\Leftrightarrow & x = \frac{-22}{63} & & \\ & V = \left\{ \frac{-22}{63} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{3}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{18}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{36}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+36} & = & \color{red}{50x} +35 \\\Leftrightarrow & 120x \color{red}{+36} \color{blue}{-36} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{-36} \\\Leftrightarrow & 120x-50x& = & 35-36 \\\Leftrightarrow & \color{red}{70} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{70} & & \\ & V = \left\{ \frac{-1}{70} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{6})& = & 3x+\frac{7}{6} \\\Leftrightarrow & -14x-\frac{35}{6}& = & 3x+\frac{7}{6} \\ & & & \text{kgv van noemers 6 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{7}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -84x \color{red}{-35} & = & \color{red}{18x} +7 \\\Leftrightarrow & -84x \color{red}{-35} \color{blue}{+35} \color{blue}{-18x} & = & \color{red}{18x} +7 \color{blue}{-18x} \color{blue}{+35} \\\Leftrightarrow & -84x-18x& = & 7+35 \\\Leftrightarrow & \color{red}{-102} x& = & 42 \\\Leftrightarrow & x = \frac{42}{-102} & & \\\Leftrightarrow & x = \frac{-7}{17} & & \\ & V = \left\{ \frac{-7}{17} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+84} & = & \color{red}{-245x} +50 \\\Leftrightarrow & 420x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +50 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 420x+245x& = & 50-84 \\\Leftrightarrow & \color{red}{665} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{665} & & \\ & V = \left\{ \frac{-34}{665} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-72}{ \color{blue}{18} }x- \frac{16}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -72x \color{red}{-16} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -72x \color{red}{-16} \color{blue}{+16} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{+16} \\\Leftrightarrow & -72x+90x& = & 45+16 \\\Leftrightarrow & \color{red}{18} x& = & 61 \\\Leftrightarrow & x = \frac{61}{18} & & \\ & V = \left\{ \frac{61}{18} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -3x+\frac{8}{9} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{180}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{-135}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-135x} +40 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +40 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & 180x+135x& = & 40+36 \\\Leftrightarrow & \color{red}{315} x& = & 76 \\\Leftrightarrow & x = \frac{76}{315} & & \\ & V = \left\{ \frac{76}{315} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{8}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-88} & = & \color{red}{385x} +30 \\\Leftrightarrow & 550x \color{red}{-88} \color{blue}{+88} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+88} \\\Leftrightarrow & 550x-385x& = & 30+88 \\\Leftrightarrow & \color{red}{165} x& = & 118 \\\Leftrightarrow & x = \frac{118}{165} & & \\ & V = \left\{ \frac{118}{165} \right\} & \\\end{align}\)