Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{-66} \\\Leftrightarrow & -462x+539x& = & 14-66 \\\Leftrightarrow & \color{red}{77} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{77} & & \\ & V = \left\{ \frac{-52}{77} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{11})& = & -8x+\frac{2}{11} \\\Leftrightarrow & -21x+\frac{14}{11}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-231}{ \color{blue}{11} }x+ \frac{14}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -231x \color{red}{+14} & = & \color{red}{-88x} +2 \\\Leftrightarrow & -231x \color{red}{+14} \color{blue}{-14} \color{blue}{+88x} & = & \color{red}{-88x} +2 \color{blue}{+88x} \color{blue}{-14} \\\Leftrightarrow & -231x+88x& = & 2-14 \\\Leftrightarrow & \color{red}{-143} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-143} & & \\\Leftrightarrow & x = \frac{12}{143} & & \\ & V = \left\{ \frac{12}{143} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{4}{5})& = & 4x+\frac{10}{3} \\\Leftrightarrow & 9x+\frac{12}{5}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{+36} & = & \color{red}{60x} +50 \\\Leftrightarrow & 135x \color{red}{+36} \color{blue}{-36} \color{blue}{-60x} & = & \color{red}{60x} +50 \color{blue}{-60x} \color{blue}{-36} \\\Leftrightarrow & 135x-60x& = & 50-36 \\\Leftrightarrow & \color{red}{75} x& = & 14 \\\Leftrightarrow & x = \frac{14}{75} & & \\ & V = \left\{ \frac{14}{75} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{3}{5})& = & 2x+\frac{8}{11} \\\Leftrightarrow & -18x-\frac{18}{5}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x- \frac{198}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{-198} & = & \color{red}{110x} +40 \\\Leftrightarrow & -990x \color{red}{-198} \color{blue}{+198} \color{blue}{-110x} & = & \color{red}{110x} +40 \color{blue}{-110x} \color{blue}{+198} \\\Leftrightarrow & -990x-110x& = & 40+198 \\\Leftrightarrow & \color{red}{-1100} x& = & 238 \\\Leftrightarrow & x = \frac{238}{-1100} & & \\\Leftrightarrow & x = \frac{-119}{550} & & \\ & V = \left\{ \frac{-119}{550} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{5})& = & 2x+\frac{4}{3} \\\Leftrightarrow & 21x+\frac{21}{5}& = & 2x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{315}{ \color{blue}{15} }x+ \frac{63}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 315x \color{red}{+63} & = & \color{red}{30x} +20 \\\Leftrightarrow & 315x \color{red}{+63} \color{blue}{-63} \color{blue}{-30x} & = & \color{red}{30x} +20 \color{blue}{-30x} \color{blue}{-63} \\\Leftrightarrow & 315x-30x& = & 20-63 \\\Leftrightarrow & \color{red}{285} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{285} & & \\ & V = \left\{ \frac{-43}{285} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{2}{3})& = & -9x+\frac{3}{4} \\\Leftrightarrow & -35x+\frac{14}{3}& = & -9x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-420}{ \color{blue}{12} }x+ \frac{56}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -420x \color{red}{+56} & = & \color{red}{-108x} +9 \\\Leftrightarrow & -420x \color{red}{+56} \color{blue}{-56} \color{blue}{+108x} & = & \color{red}{-108x} +9 \color{blue}{+108x} \color{blue}{-56} \\\Leftrightarrow & -420x+108x& = & 9-56 \\\Leftrightarrow & \color{red}{-312} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{-312} & & \\\Leftrightarrow & x = \frac{47}{312} & & \\ & V = \left\{ \frac{47}{312} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -35x-4& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x- \frac{20}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{-20} & = & \color{red}{45x} +6 \\\Leftrightarrow & -175x \color{red}{-20} \color{blue}{+20} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+20} \\\Leftrightarrow & -175x-45x& = & 6+20 \\\Leftrightarrow & \color{red}{-220} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-220} & & \\\Leftrightarrow & x = \frac{-13}{110} & & \\ & V = \left\{ \frac{-13}{110} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{24}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{120}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-120} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 1050x \color{red}{-120} \color{blue}{+120} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+120} \\\Leftrightarrow & 1050x+245x& = & 42+120 \\\Leftrightarrow & \color{red}{1295} x& = & 162 \\\Leftrightarrow & x = \frac{162}{1295} & & \\ & V = \left\{ \frac{162}{1295} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{9})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 4x-\frac{4}{9}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{36}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{12}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 36x \color{red}{-4} & = & \color{red}{63x} +12 \\\Leftrightarrow & 36x \color{red}{-4} \color{blue}{+4} \color{blue}{-63x} & = & \color{red}{63x} +12 \color{blue}{-63x} \color{blue}{+4} \\\Leftrightarrow & 36x-63x& = & 12+4 \\\Leftrightarrow & \color{red}{-27} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-27} & & \\\Leftrightarrow & x = \frac{-16}{27} & & \\ & V = \left\{ \frac{-16}{27} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{20}{7}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+220} & = & \color{red}{693x} +56 \\\Leftrightarrow & -616x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +56 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & -616x-693x& = & 56-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{-1309} & & \\\Leftrightarrow & x = \frac{164}{1309} & & \\ & V = \left\{ \frac{164}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 4x-\frac{10}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-70} & = & \color{red}{385x} +110 \\\Leftrightarrow & 308x \color{red}{-70} \color{blue}{+70} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{+70} \\\Leftrightarrow & 308x-385x& = & 110+70 \\\Leftrightarrow & \color{red}{-77} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-77} & & \\\Leftrightarrow & x = \frac{-180}{77} & & \\ & V = \left\{ \frac{-180}{77} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{2}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-8} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -100x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & -100x+70x& = & 45+8 \\\Leftrightarrow & \color{red}{-30} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-30} & & \\\Leftrightarrow & x = \frac{-53}{30} & & \\ & V = \left\{ \frac{-53}{30} \right\} & \\\end{align}\)