Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{2})& = & 2x+\frac{3}{4} \\\Leftrightarrow & 15x+\frac{25}{2}& = & 2x+\frac{3}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{50}{ \color{blue}{4} })& = & (\frac{8}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+50} & = & \color{red}{8x} +3 \\\Leftrightarrow & 60x \color{red}{+50} \color{blue}{-50} \color{blue}{-8x} & = & \color{red}{8x} +3 \color{blue}{-8x} \color{blue}{-50} \\\Leftrightarrow & 60x-8x& = & 3-50 \\\Leftrightarrow & \color{red}{52} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{52} & & \\ & V = \left\{ \frac{-47}{52} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{5}{6})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -20x+\frac{25}{6}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{75}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+75} & = & \color{red}{126x} +20 \\\Leftrightarrow & -360x \color{red}{+75} \color{blue}{-75} \color{blue}{-126x} & = & \color{red}{126x} +20 \color{blue}{-126x} \color{blue}{-75} \\\Leftrightarrow & -360x-126x& = & 20-75 \\\Leftrightarrow & \color{red}{-486} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-486} & & \\\Leftrightarrow & x = \frac{55}{486} & & \\ & V = \left\{ \frac{55}{486} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 4x+\frac{8}{3} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{27}{ \color{blue}{15} })& = & (\frac{60}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-27} & = & \color{red}{60x} +40 \\\Leftrightarrow & 135x \color{red}{-27} \color{blue}{+27} \color{blue}{-60x} & = & \color{red}{60x} +40 \color{blue}{-60x} \color{blue}{+27} \\\Leftrightarrow & 135x-60x& = & 40+27 \\\Leftrightarrow & \color{red}{75} x& = & 67 \\\Leftrightarrow & x = \frac{67}{75} & & \\ & V = \left\{ \frac{67}{75} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{3}{11})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2970}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2970x \color{red}{+162} & = & \color{red}{-693x} +88 \\\Leftrightarrow & -2970x \color{red}{+162} \color{blue}{-162} \color{blue}{+693x} & = & \color{red}{-693x} +88 \color{blue}{+693x} \color{blue}{-162} \\\Leftrightarrow & -2970x+693x& = & 88-162 \\\Leftrightarrow & \color{red}{-2277} x& = & -74 \\\Leftrightarrow & x = \frac{-74}{-2277} & & \\\Leftrightarrow & x = \frac{74}{2277} & & \\ & V = \left\{ \frac{74}{2277} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & 3x+\frac{4}{7} \\\Leftrightarrow & 8x-\frac{16}{7}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{21}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{-16} & = & \color{red}{21x} +4 \\\Leftrightarrow & 56x \color{red}{-16} \color{blue}{+16} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+16} \\\Leftrightarrow & 56x-21x& = & 4+16 \\\Leftrightarrow & \color{red}{35} x& = & 20 \\\Leftrightarrow & x = \frac{20}{35} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x-\frac{8}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{72}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-72} & = & \color{red}{693x} +44 \\\Leftrightarrow & -990x \color{red}{-72} \color{blue}{+72} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+72} \\\Leftrightarrow & -990x-693x& = & 44+72 \\\Leftrightarrow & \color{red}{-1683} x& = & 116 \\\Leftrightarrow & x = \frac{116}{-1683} & & \\\Leftrightarrow & x = \frac{-116}{1683} & & \\ & V = \left\{ \frac{-116}{1683} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{5}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 28x-\frac{35}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x- \frac{35}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{-35} & = & \color{red}{-33x} +6 \\\Leftrightarrow & 308x \color{red}{-35} \color{blue}{+35} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{+35} \\\Leftrightarrow & 308x+33x& = & 6+35 \\\Leftrightarrow & \color{red}{341} x& = & 41 \\\Leftrightarrow & x = \frac{41}{341} & & \\ & V = \left\{ \frac{41}{341} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{7})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{10}{7}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+30} & = & \color{red}{147x} +14 \\\Leftrightarrow & 126x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +14 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & 126x-147x& = & 14-30 \\\Leftrightarrow & \color{red}{-21} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-21} & & \\\Leftrightarrow & x = \frac{16}{21} & & \\ & V = \left\{ \frac{16}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{8})& = & -4x+\frac{4}{3} \\\Leftrightarrow & 25x-\frac{15}{8}& = & -4x+\frac{4}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{600}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{32}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 600x \color{red}{-45} & = & \color{red}{-96x} +32 \\\Leftrightarrow & 600x \color{red}{-45} \color{blue}{+45} \color{blue}{+96x} & = & \color{red}{-96x} +32 \color{blue}{+96x} \color{blue}{+45} \\\Leftrightarrow & 600x+96x& = & 32+45 \\\Leftrightarrow & \color{red}{696} x& = & 77 \\\Leftrightarrow & x = \frac{77}{696} & & \\ & V = \left\{ \frac{77}{696} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{7})& = & -7x+\frac{7}{8} \\\Leftrightarrow & 25x+\frac{20}{7}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1400}{ \color{blue}{56} }x+ \frac{160}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1400x \color{red}{+160} & = & \color{red}{-392x} +49 \\\Leftrightarrow & 1400x \color{red}{+160} \color{blue}{-160} \color{blue}{+392x} & = & \color{red}{-392x} +49 \color{blue}{+392x} \color{blue}{-160} \\\Leftrightarrow & 1400x+392x& = & 49-160 \\\Leftrightarrow & \color{red}{1792} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{1792} & & \\ & V = \left\{ \frac{-111}{1792} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & 2x+\frac{8}{3} \\\Leftrightarrow & 15x-\frac{20}{3}& = & 2x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 45x \color{red}{-20} & = & \color{red}{6x} +8 \\\Leftrightarrow & 45x \color{red}{-20} \color{blue}{+20} \color{blue}{-6x} & = & \color{red}{6x} +8 \color{blue}{-6x} \color{blue}{+20} \\\Leftrightarrow & 45x-6x& = & 8+20 \\\Leftrightarrow & \color{red}{39} x& = & 28 \\\Leftrightarrow & x = \frac{28}{39} & & \\ & V = \left\{ \frac{28}{39} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{10})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 15x-\frac{9}{10}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 10 en 7 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x- \frac{63}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{90}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{-63} & = & \color{red}{490x} +90 \\\Leftrightarrow & 1050x \color{red}{-63} \color{blue}{+63} \color{blue}{-490x} & = & \color{red}{490x} +90 \color{blue}{-490x} \color{blue}{+63} \\\Leftrightarrow & 1050x-490x& = & 90+63 \\\Leftrightarrow & \color{red}{560} x& = & 153 \\\Leftrightarrow & x = \frac{153}{560} & & \\ & V = \left\{ \frac{153}{560} \right\} & \\\end{align}\)