Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{11})& = & 2x+\frac{9}{8} \\\Leftrightarrow & 21x-\frac{28}{11}& = & 2x+\frac{9}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1848}{ \color{blue}{88} }x- \frac{224}{ \color{blue}{88} })& = & (\frac{176}{ \color{blue}{88} }x+ \frac{99}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1848x \color{red}{-224} & = & \color{red}{176x} +99 \\\Leftrightarrow & 1848x \color{red}{-224} \color{blue}{+224} \color{blue}{-176x} & = & \color{red}{176x} +99 \color{blue}{-176x} \color{blue}{+224} \\\Leftrightarrow & 1848x-176x& = & 99+224 \\\Leftrightarrow & \color{red}{1672} x& = & 323 \\\Leftrightarrow & x = \frac{323}{1672} & & \\\Leftrightarrow & x = \frac{17}{88} & & \\ & V = \left\{ \frac{17}{88} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 3x+\frac{6}{11} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-990}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{165}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -990x \color{red}{+132} & = & \color{red}{165x} +30 \\\Leftrightarrow & -990x \color{red}{+132} \color{blue}{-132} \color{blue}{-165x} & = & \color{red}{165x} +30 \color{blue}{-165x} \color{blue}{-132} \\\Leftrightarrow & -990x-165x& = & 30-132 \\\Leftrightarrow & \color{red}{-1155} x& = & -102 \\\Leftrightarrow & x = \frac{-102}{-1155} & & \\\Leftrightarrow & x = \frac{34}{385} & & \\ & V = \left\{ \frac{34}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{2}{11})& = & 7x+\frac{3}{11} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{275}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 275x \color{red}{-10} & = & \color{red}{77x} +3 \\\Leftrightarrow & 275x \color{red}{-10} \color{blue}{+10} \color{blue}{-77x} & = & \color{red}{77x} +3 \color{blue}{-77x} \color{blue}{+10} \\\Leftrightarrow & 275x-77x& = & 3+10 \\\Leftrightarrow & \color{red}{198} x& = & 13 \\\Leftrightarrow & x = \frac{13}{198} & & \\ & V = \left\{ \frac{13}{198} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{9})& = & 3x+\frac{9}{4} \\\Leftrightarrow & -20x-\frac{8}{9}& = & 3x+\frac{9}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-720}{ \color{blue}{36} }x- \frac{32}{ \color{blue}{36} })& = & (\frac{108}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -720x \color{red}{-32} & = & \color{red}{108x} +81 \\\Leftrightarrow & -720x \color{red}{-32} \color{blue}{+32} \color{blue}{-108x} & = & \color{red}{108x} +81 \color{blue}{-108x} \color{blue}{+32} \\\Leftrightarrow & -720x-108x& = & 81+32 \\\Leftrightarrow & \color{red}{-828} x& = & 113 \\\Leftrightarrow & x = \frac{113}{-828} & & \\\Leftrightarrow & x = \frac{-113}{828} & & \\ & V = \left\{ \frac{-113}{828} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & -9x+\frac{5}{7} \\\Leftrightarrow & 20x+\frac{16}{3}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{112}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+112} & = & \color{red}{-189x} +15 \\\Leftrightarrow & 420x \color{red}{+112} \color{blue}{-112} \color{blue}{+189x} & = & \color{red}{-189x} +15 \color{blue}{+189x} \color{blue}{-112} \\\Leftrightarrow & 420x+189x& = & 15-112 \\\Leftrightarrow & \color{red}{609} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{609} & & \\ & V = \left\{ \frac{-97}{609} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{3})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -20x-\frac{20}{3}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-120}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -120x \color{red}{-40} & = & \color{red}{18x} +27 \\\Leftrightarrow & -120x \color{red}{-40} \color{blue}{+40} \color{blue}{-18x} & = & \color{red}{18x} +27 \color{blue}{-18x} \color{blue}{+40} \\\Leftrightarrow & -120x-18x& = & 27+40 \\\Leftrightarrow & \color{red}{-138} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-138} & & \\\Leftrightarrow & x = \frac{-67}{138} & & \\ & V = \left\{ \frac{-67}{138} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & -9x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -9x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{-27x} +7 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{+27x} & = & \color{red}{-27x} +7 \color{blue}{+27x} \color{blue}{-20} \\\Leftrightarrow & 60x+27x& = & 7-20 \\\Leftrightarrow & \color{red}{87} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{87} & & \\ & V = \left\{ \frac{-13}{87} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{11})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 8x-\frac{12}{11}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-12} & = & \color{red}{99x} +10 \\\Leftrightarrow & 88x \color{red}{-12} \color{blue}{+12} \color{blue}{-99x} & = & \color{red}{99x} +10 \color{blue}{-99x} \color{blue}{+12} \\\Leftrightarrow & 88x-99x& = & 10+12 \\\Leftrightarrow & \color{red}{-11} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-11} & & \\\Leftrightarrow & x = -2 & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{2})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{21}{2}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{63}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+63} & = & \color{red}{-42x} +20 \\\Leftrightarrow & -168x \color{red}{+63} \color{blue}{-63} \color{blue}{+42x} & = & \color{red}{-42x} +20 \color{blue}{+42x} \color{blue}{-63} \\\Leftrightarrow & -168x+42x& = & 20-63 \\\Leftrightarrow & \color{red}{-126} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-126} & & \\\Leftrightarrow & x = \frac{43}{126} & & \\ & V = \left\{ \frac{43}{126} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{4}{5})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -16x-\frac{16}{5}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{176}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-176} & = & \color{red}{385x} +50 \\\Leftrightarrow & -880x \color{red}{-176} \color{blue}{+176} \color{blue}{-385x} & = & \color{red}{385x} +50 \color{blue}{-385x} \color{blue}{+176} \\\Leftrightarrow & -880x-385x& = & 50+176 \\\Leftrightarrow & \color{red}{-1265} x& = & 226 \\\Leftrightarrow & x = \frac{226}{-1265} & & \\\Leftrightarrow & x = \frac{-226}{1265} & & \\ & V = \left\{ \frac{-226}{1265} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{3}{5})& = & 9x+\frac{9}{5} \\\Leftrightarrow & -35x-\frac{21}{5}& = & 9x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x- \frac{21}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{-21} & = & \color{red}{45x} +9 \\\Leftrightarrow & -175x \color{red}{-21} \color{blue}{+21} \color{blue}{-45x} & = & \color{red}{45x} +9 \color{blue}{-45x} \color{blue}{+21} \\\Leftrightarrow & -175x-45x& = & 9+21 \\\Leftrightarrow & \color{red}{-220} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-220} & & \\\Leftrightarrow & x = \frac{-3}{22} & & \\ & V = \left\{ \frac{-3}{22} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{2}{5})& = & 5x+\frac{8}{9} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{+108} & = & \color{red}{225x} +40 \\\Leftrightarrow & 540x \color{red}{+108} \color{blue}{-108} \color{blue}{-225x} & = & \color{red}{225x} +40 \color{blue}{-225x} \color{blue}{-108} \\\Leftrightarrow & 540x-225x& = & 40-108 \\\Leftrightarrow & \color{red}{315} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{315} & & \\ & V = \left\{ \frac{-68}{315} \right\} & \\\end{align}\)