Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{5})& = & -3x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{8}{5}& = & -3x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{88}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-88} & = & \color{red}{-165x} +50 \\\Leftrightarrow & 550x \color{red}{-88} \color{blue}{+88} \color{blue}{+165x} & = & \color{red}{-165x} +50 \color{blue}{+165x} \color{blue}{+88} \\\Leftrightarrow & 550x+165x& = & 50+88 \\\Leftrightarrow & \color{red}{715} x& = & 138 \\\Leftrightarrow & x = \frac{138}{715} & & \\ & V = \left\{ \frac{138}{715} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & 9x+\frac{10}{11} \\\Leftrightarrow & -20x+\frac{15}{8}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1760}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{792}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1760x \color{red}{+165} & = & \color{red}{792x} +80 \\\Leftrightarrow & -1760x \color{red}{+165} \color{blue}{-165} \color{blue}{-792x} & = & \color{red}{792x} +80 \color{blue}{-792x} \color{blue}{-165} \\\Leftrightarrow & -1760x-792x& = & 80-165 \\\Leftrightarrow & \color{red}{-2552} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{-2552} & & \\\Leftrightarrow & x = \frac{85}{2552} & & \\ & V = \left\{ \frac{85}{2552} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{3})& = & -8x+\frac{5}{4} \\\Leftrightarrow & -21x+\frac{28}{3}& = & -8x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{112}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+112} & = & \color{red}{-96x} +15 \\\Leftrightarrow & -252x \color{red}{+112} \color{blue}{-112} \color{blue}{+96x} & = & \color{red}{-96x} +15 \color{blue}{+96x} \color{blue}{-112} \\\Leftrightarrow & -252x+96x& = & 15-112 \\\Leftrightarrow & \color{red}{-156} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-156} & & \\\Leftrightarrow & x = \frac{97}{156} & & \\ & V = \left\{ \frac{97}{156} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{3}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 10x+\frac{6}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 70x \color{red}{+6} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 70x \color{red}{+6} \color{blue}{-6} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{-6} \\\Leftrightarrow & 70x+21x& = & 3-6 \\\Leftrightarrow & \color{red}{91} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{91} & & \\ & V = \left\{ \frac{-3}{91} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{2}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{6}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+6} & = & \color{red}{35x} +10 \\\Leftrightarrow & 84x \color{red}{+6} \color{blue}{-6} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{-6} \\\Leftrightarrow & 84x-35x& = & 10-6 \\\Leftrightarrow & \color{red}{49} x& = & 4 \\\Leftrightarrow & x = \frac{4}{49} & & \\ & V = \left\{ \frac{4}{49} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{5}{8})& = & -4x+\frac{9}{8} \\\Leftrightarrow & -15x+\frac{15}{8}& = & -4x+\frac{9}{8} \\ & & & \text{kgv van noemers 8 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-120}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-32}{ \color{blue}{8} }x+ \frac{9}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -120x \color{red}{+15} & = & \color{red}{-32x} +9 \\\Leftrightarrow & -120x \color{red}{+15} \color{blue}{-15} \color{blue}{+32x} & = & \color{red}{-32x} +9 \color{blue}{+32x} \color{blue}{-15} \\\Leftrightarrow & -120x+32x& = & 9-15 \\\Leftrightarrow & \color{red}{-88} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-88} & & \\\Leftrightarrow & x = \frac{3}{44} & & \\ & V = \left\{ \frac{3}{44} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{9})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 16x-\frac{16}{9}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{16}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-16} & = & \color{red}{-27x} +24 \\\Leftrightarrow & 144x \color{red}{-16} \color{blue}{+16} \color{blue}{+27x} & = & \color{red}{-27x} +24 \color{blue}{+27x} \color{blue}{+16} \\\Leftrightarrow & 144x+27x& = & 24+16 \\\Leftrightarrow & \color{red}{171} x& = & 40 \\\Leftrightarrow & x = \frac{40}{171} & & \\ & V = \left\{ \frac{40}{171} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{11})& = & -8x+\frac{6}{11} \\\Leftrightarrow & -15x-\frac{15}{11}& = & -8x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{15}{ \color{blue}{11} })& = & (\frac{-88}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-15} & = & \color{red}{-88x} +6 \\\Leftrightarrow & -165x \color{red}{-15} \color{blue}{+15} \color{blue}{+88x} & = & \color{red}{-88x} +6 \color{blue}{+88x} \color{blue}{+15} \\\Leftrightarrow & -165x+88x& = & 6+15 \\\Leftrightarrow & \color{red}{-77} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-77} & & \\\Leftrightarrow & x = \frac{-3}{11} & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{1}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & -14x+\frac{7}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+35} & = & \color{red}{-45x} +18 \\\Leftrightarrow & -210x \color{red}{+35} \color{blue}{-35} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{-35} \\\Leftrightarrow & -210x+45x& = & 18-35 \\\Leftrightarrow & \color{red}{-165} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-165} & & \\\Leftrightarrow & x = \frac{17}{165} & & \\ & V = \left\{ \frac{17}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{7})& = & 5x+\frac{9}{11} \\\Leftrightarrow & 16x+\frac{16}{7}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+176} & = & \color{red}{385x} +63 \\\Leftrightarrow & 1232x \color{red}{+176} \color{blue}{-176} \color{blue}{-385x} & = & \color{red}{385x} +63 \color{blue}{-385x} \color{blue}{-176} \\\Leftrightarrow & 1232x-385x& = & 63-176 \\\Leftrightarrow & \color{red}{847} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{847} & & \\ & V = \left\{ \frac{-113}{847} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{9})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{891x} +72 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{-891x} & = & \color{red}{891x} +72 \color{blue}{-891x} \color{blue}{-88} \\\Leftrightarrow & -792x-891x& = & 72-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-1683} & & \\\Leftrightarrow & x = \frac{16}{1683} & & \\ & V = \left\{ \frac{16}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{2})& = & -3x+\frac{5}{2} \\\Leftrightarrow & 20x-\frac{25}{2}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{40}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{-6}{ \color{blue}{2} }x+ \frac{5}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 40x \color{red}{-25} & = & \color{red}{-6x} +5 \\\Leftrightarrow & 40x \color{red}{-25} \color{blue}{+25} \color{blue}{+6x} & = & \color{red}{-6x} +5 \color{blue}{+6x} \color{blue}{+25} \\\Leftrightarrow & 40x+6x& = & 5+25 \\\Leftrightarrow & \color{red}{46} x& = & 30 \\\Leftrightarrow & x = \frac{30}{46} & & \\\Leftrightarrow & x = \frac{15}{23} & & \\ & V = \left\{ \frac{15}{23} \right\} & \\\end{align}\)