Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{4}{9})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{8}{9}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-54}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -54x \color{red}{-8} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -54x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -54x+63x& = & 4+8 \\\Leftrightarrow & \color{red}{9} x& = & 12 \\\Leftrightarrow & x = \frac{12}{9} & & \\\Leftrightarrow & x = \frac{4}{3} & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{4}{11})& = & -5x+\frac{4}{9} \\\Leftrightarrow & -4x+\frac{8}{11}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-396}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -396x \color{red}{+72} & = & \color{red}{-495x} +44 \\\Leftrightarrow & -396x \color{red}{+72} \color{blue}{-72} \color{blue}{+495x} & = & \color{red}{-495x} +44 \color{blue}{+495x} \color{blue}{-72} \\\Leftrightarrow & -396x+495x& = & 44-72 \\\Leftrightarrow & \color{red}{99} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{99} & & \\ & V = \left\{ \frac{-28}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & 3x+\frac{8}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{45x} +40 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{-45x} & = & \color{red}{45x} +40 \color{blue}{-45x} \color{blue}{+36} \\\Leftrightarrow & -120x-45x& = & 40+36 \\\Leftrightarrow & \color{red}{-165} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-165} & & \\\Leftrightarrow & x = \frac{-76}{165} & & \\ & V = \left\{ \frac{-76}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{8})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 6x+\frac{9}{8}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{336}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 336x \color{red}{+63} & = & \color{red}{-280x} +72 \\\Leftrightarrow & 336x \color{red}{+63} \color{blue}{-63} \color{blue}{+280x} & = & \color{red}{-280x} +72 \color{blue}{+280x} \color{blue}{-63} \\\Leftrightarrow & 336x+280x& = & 72-63 \\\Leftrightarrow & \color{red}{616} x& = & 9 \\\Leftrightarrow & x = \frac{9}{616} & & \\ & V = \left\{ \frac{9}{616} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & -3x+\frac{3}{4} \\\Leftrightarrow & -20x-\frac{10}{7}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{40}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-40} & = & \color{red}{-84x} +21 \\\Leftrightarrow & -560x \color{red}{-40} \color{blue}{+40} \color{blue}{+84x} & = & \color{red}{-84x} +21 \color{blue}{+84x} \color{blue}{+40} \\\Leftrightarrow & -560x+84x& = & 21+40 \\\Leftrightarrow & \color{red}{-476} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-476} & & \\\Leftrightarrow & x = \frac{-61}{476} & & \\ & V = \left\{ \frac{-61}{476} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{12}{5}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{+36} & = & \color{red}{75x} +10 \\\Leftrightarrow & 240x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +10 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & 240x-75x& = & 10-36 \\\Leftrightarrow & \color{red}{165} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{165} & & \\ & V = \left\{ \frac{-26}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{110}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+132} & = & \color{red}{110x} +40 \\\Leftrightarrow & 825x \color{red}{+132} \color{blue}{-132} \color{blue}{-110x} & = & \color{red}{110x} +40 \color{blue}{-110x} \color{blue}{-132} \\\Leftrightarrow & 825x-110x& = & 40-132 \\\Leftrightarrow & \color{red}{715} x& = & -92 \\\Leftrightarrow & x = \frac{-92}{715} & & \\ & V = \left\{ \frac{-92}{715} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{10}{9} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-108} & = & \color{red}{495x} +110 \\\Leftrightarrow & -1188x \color{red}{-108} \color{blue}{+108} \color{blue}{-495x} & = & \color{red}{495x} +110 \color{blue}{-495x} \color{blue}{+108} \\\Leftrightarrow & -1188x-495x& = & 110+108 \\\Leftrightarrow & \color{red}{-1683} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-1683} & & \\\Leftrightarrow & x = \frac{-218}{1683} & & \\ & V = \left\{ \frac{-218}{1683} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x-\frac{9}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{18}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-18} & = & \color{red}{50x} +35 \\\Leftrightarrow & 120x \color{red}{-18} \color{blue}{+18} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{+18} \\\Leftrightarrow & 120x-50x& = & 35+18 \\\Leftrightarrow & \color{red}{70} x& = & 53 \\\Leftrightarrow & x = \frac{53}{70} & & \\ & V = \left\{ \frac{53}{70} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{5}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & 8x-\frac{10}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{176}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 176x \color{red}{-20} & = & \color{red}{110x} +33 \\\Leftrightarrow & 176x \color{red}{-20} \color{blue}{+20} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{+20} \\\Leftrightarrow & 176x-110x& = & 33+20 \\\Leftrightarrow & \color{red}{66} x& = & 53 \\\Leftrightarrow & x = \frac{53}{66} & & \\ & V = \left\{ \frac{53}{66} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{2}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x-\frac{6}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-18} & = & \color{red}{-165x} +88 \\\Leftrightarrow & -396x \color{red}{-18} \color{blue}{+18} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+18} \\\Leftrightarrow & -396x+165x& = & 88+18 \\\Leftrightarrow & \color{red}{-231} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-231} & & \\\Leftrightarrow & x = \frac{-106}{231} & & \\ & V = \left\{ \frac{-106}{231} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{9}{8} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{672}{ \color{blue}{56} }x- \frac{128}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{63}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 672x \color{red}{-128} & = & \color{red}{-280x} +63 \\\Leftrightarrow & 672x \color{red}{-128} \color{blue}{+128} \color{blue}{+280x} & = & \color{red}{-280x} +63 \color{blue}{+280x} \color{blue}{+128} \\\Leftrightarrow & 672x+280x& = & 63+128 \\\Leftrightarrow & \color{red}{952} x& = & 191 \\\Leftrightarrow & x = \frac{191}{952} & & \\ & V = \left\{ \frac{191}{952} \right\} & \\\end{align}\)