Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{3})& = & 3x+\frac{10}{11} \\\Leftrightarrow & 8x-\frac{20}{3}& = & 3x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{-220} & = & \color{red}{99x} +30 \\\Leftrightarrow & 264x \color{red}{-220} \color{blue}{+220} \color{blue}{-99x} & = & \color{red}{99x} +30 \color{blue}{-99x} \color{blue}{+220} \\\Leftrightarrow & 264x-99x& = & 30+220 \\\Leftrightarrow & \color{red}{165} x& = & 250 \\\Leftrightarrow & x = \frac{250}{165} & & \\\Leftrightarrow & x = \frac{50}{33} & & \\ & V = \left\{ \frac{50}{33} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{3}{5})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 20x+\frac{12}{5}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{135}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+36} & = & \color{red}{135x} +50 \\\Leftrightarrow & 300x \color{red}{+36} \color{blue}{-36} \color{blue}{-135x} & = & \color{red}{135x} +50 \color{blue}{-135x} \color{blue}{-36} \\\Leftrightarrow & 300x-135x& = & 50-36 \\\Leftrightarrow & \color{red}{165} x& = & 14 \\\Leftrightarrow & x = \frac{14}{165} & & \\ & V = \left\{ \frac{14}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{3})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+8} & = & \color{red}{15x} +7 \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-15x} & = & \color{red}{15x} +7 \color{blue}{-15x} \color{blue}{-8} \\\Leftrightarrow & 24x-15x& = & 7-8 \\\Leftrightarrow & \color{red}{9} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{9} & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & -4x+\frac{4}{5} \\\Leftrightarrow & -15x+\frac{9}{5}& = & -4x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{+9} & = & \color{red}{-20x} +4 \\\Leftrightarrow & -75x \color{red}{+9} \color{blue}{-9} \color{blue}{+20x} & = & \color{red}{-20x} +4 \color{blue}{+20x} \color{blue}{-9} \\\Leftrightarrow & -75x+20x& = & 4-9 \\\Leftrightarrow & \color{red}{-55} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-55} & & \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{8})& = & 5x+\frac{6}{7} \\\Leftrightarrow & -14x-\frac{21}{8}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-784}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -784x \color{red}{-147} & = & \color{red}{280x} +48 \\\Leftrightarrow & -784x \color{red}{-147} \color{blue}{+147} \color{blue}{-280x} & = & \color{red}{280x} +48 \color{blue}{-280x} \color{blue}{+147} \\\Leftrightarrow & -784x-280x& = & 48+147 \\\Leftrightarrow & \color{red}{-1064} x& = & 195 \\\Leftrightarrow & x = \frac{195}{-1064} & & \\\Leftrightarrow & x = \frac{-195}{1064} & & \\ & V = \left\{ \frac{-195}{1064} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{1}{3})& = & 5x+\frac{10}{11} \\\Leftrightarrow & -14x+\frac{7}{3}& = & 5x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{+77} & = & \color{red}{165x} +30 \\\Leftrightarrow & -462x \color{red}{+77} \color{blue}{-77} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{-77} \\\Leftrightarrow & -462x-165x& = & 30-77 \\\Leftrightarrow & \color{red}{-627} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-627} & & \\\Leftrightarrow & x = \frac{47}{627} & & \\ & V = \left\{ \frac{47}{627} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{11})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{12}{11}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-12} & = & \color{red}{-33x} +4 \\\Leftrightarrow & -88x \color{red}{-12} \color{blue}{+12} \color{blue}{+33x} & = & \color{red}{-33x} +4 \color{blue}{+33x} \color{blue}{+12} \\\Leftrightarrow & -88x+33x& = & 4+12 \\\Leftrightarrow & \color{red}{-55} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-55} & & \\\Leftrightarrow & x = \frac{-16}{55} & & \\ & V = \left\{ \frac{-16}{55} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{3}{5})& = & 3x+\frac{7}{4} \\\Leftrightarrow & -14x-\frac{21}{5}& = & 3x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-280}{ \color{blue}{20} }x- \frac{84}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{60x} +35 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{-60x} & = & \color{red}{60x} +35 \color{blue}{-60x} \color{blue}{+84} \\\Leftrightarrow & -280x-60x& = & 35+84 \\\Leftrightarrow & \color{red}{-340} x& = & 119 \\\Leftrightarrow & x = \frac{119}{-340} & & \\\Leftrightarrow & x = \frac{-7}{20} & & \\ & V = \left\{ \frac{-7}{20} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & 5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{16}{3}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+16} & = & \color{red}{15x} +10 \\\Leftrightarrow & 36x \color{red}{+16} \color{blue}{-16} \color{blue}{-15x} & = & \color{red}{15x} +10 \color{blue}{-15x} \color{blue}{-16} \\\Leftrightarrow & 36x-15x& = & 10-16 \\\Leftrightarrow & \color{red}{21} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{21} & & \\\Leftrightarrow & x = \frac{-2}{7} & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & 10x-\frac{15}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{210}{ \color{blue}{21} }x- \frac{45}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 210x \color{red}{-45} & = & \color{red}{147x} +35 \\\Leftrightarrow & 210x \color{red}{-45} \color{blue}{+45} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+45} \\\Leftrightarrow & 210x-147x& = & 35+45 \\\Leftrightarrow & \color{red}{63} x& = & 80 \\\Leftrightarrow & x = \frac{80}{63} & & \\ & V = \left\{ \frac{80}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -5x+\frac{8}{11} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-66} & = & \color{red}{-385x} +56 \\\Leftrightarrow & 308x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +56 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & 308x+385x& = & 56+66 \\\Leftrightarrow & \color{red}{693} x& = & 122 \\\Leftrightarrow & x = \frac{122}{693} & & \\ & V = \left\{ \frac{122}{693} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{9})& = & -7x+\frac{5}{2} \\\Leftrightarrow & 10x+\frac{20}{9}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{180}{ \color{blue}{18} }x+ \frac{40}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 180x \color{red}{+40} & = & \color{red}{-126x} +45 \\\Leftrightarrow & 180x \color{red}{+40} \color{blue}{-40} \color{blue}{+126x} & = & \color{red}{-126x} +45 \color{blue}{+126x} \color{blue}{-40} \\\Leftrightarrow & 180x+126x& = & 45-40 \\\Leftrightarrow & \color{red}{306} x& = & 5 \\\Leftrightarrow & x = \frac{5}{306} & & \\ & V = \left\{ \frac{5}{306} \right\} & \\\end{align}\)