Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{5}{9})& = & -4x+\frac{8}{11} \\\Leftrightarrow & 21x+\frac{35}{9}& = & -4x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{-396}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{+385} & = & \color{red}{-396x} +72 \\\Leftrightarrow & 2079x \color{red}{+385} \color{blue}{-385} \color{blue}{+396x} & = & \color{red}{-396x} +72 \color{blue}{+396x} \color{blue}{-385} \\\Leftrightarrow & 2079x+396x& = & 72-385 \\\Leftrightarrow & \color{red}{2475} x& = & -313 \\\Leftrightarrow & x = \frac{-313}{2475} & & \\ & V = \left\{ \frac{-313}{2475} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -6x-\frac{12}{5}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-210}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -210x \color{red}{-84} & = & \color{red}{-245x} +40 \\\Leftrightarrow & -210x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +40 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & -210x+245x& = & 40+84 \\\Leftrightarrow & \color{red}{35} x& = & 124 \\\Leftrightarrow & x = \frac{124}{35} & & \\ & V = \left\{ \frac{124}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -7x+\frac{3}{5} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{+6} & = & \color{red}{-35x} +3 \\\Leftrightarrow & 75x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 75x+35x& = & 3-6 \\\Leftrightarrow & \color{red}{110} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{110} & & \\ & V = \left\{ \frac{-3}{110} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{4}{3})& = & -3x+\frac{5}{8} \\\Leftrightarrow & 28x+\frac{28}{3}& = & -3x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x+ \frac{224}{ \color{blue}{24} })& = & (\frac{-72}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{+224} & = & \color{red}{-72x} +15 \\\Leftrightarrow & 672x \color{red}{+224} \color{blue}{-224} \color{blue}{+72x} & = & \color{red}{-72x} +15 \color{blue}{+72x} \color{blue}{-224} \\\Leftrightarrow & 672x+72x& = & 15-224 \\\Leftrightarrow & \color{red}{744} x& = & -209 \\\Leftrightarrow & x = \frac{-209}{744} & & \\ & V = \left\{ \frac{-209}{744} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{2})& = & -2x+\frac{5}{9} \\\Leftrightarrow & -25x-\frac{25}{2}& = & -2x+\frac{5}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-450}{ \color{blue}{18} }x- \frac{225}{ \color{blue}{18} })& = & (\frac{-36}{ \color{blue}{18} }x+ \frac{10}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -450x \color{red}{-225} & = & \color{red}{-36x} +10 \\\Leftrightarrow & -450x \color{red}{-225} \color{blue}{+225} \color{blue}{+36x} & = & \color{red}{-36x} +10 \color{blue}{+36x} \color{blue}{+225} \\\Leftrightarrow & -450x+36x& = & 10+225 \\\Leftrightarrow & \color{red}{-414} x& = & 235 \\\Leftrightarrow & x = \frac{235}{-414} & & \\\Leftrightarrow & x = \frac{-235}{414} & & \\ & V = \left\{ \frac{-235}{414} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{5}{9})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -10x-\frac{10}{9}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x- \frac{110}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{-110} & = & \color{red}{693x} +90 \\\Leftrightarrow & -990x \color{red}{-110} \color{blue}{+110} \color{blue}{-693x} & = & \color{red}{693x} +90 \color{blue}{-693x} \color{blue}{+110} \\\Leftrightarrow & -990x-693x& = & 90+110 \\\Leftrightarrow & \color{red}{-1683} x& = & 200 \\\Leftrightarrow & x = \frac{200}{-1683} & & \\\Leftrightarrow & x = \frac{-200}{1683} & & \\ & V = \left\{ \frac{-200}{1683} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{10})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -6x+\frac{9}{10}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-540}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{20}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -540x \color{red}{+81} & = & \color{red}{-630x} +20 \\\Leftrightarrow & -540x \color{red}{+81} \color{blue}{-81} \color{blue}{+630x} & = & \color{red}{-630x} +20 \color{blue}{+630x} \color{blue}{-81} \\\Leftrightarrow & -540x+630x& = & 20-81 \\\Leftrightarrow & \color{red}{90} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{90} & & \\ & V = \left\{ \frac{-61}{90} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{7})& = & -5x+\frac{2}{9} \\\Leftrightarrow & 9x+\frac{6}{7}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{567}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 567x \color{red}{+54} & = & \color{red}{-315x} +14 \\\Leftrightarrow & 567x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +14 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & 567x+315x& = & 14-54 \\\Leftrightarrow & \color{red}{882} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{882} & & \\\Leftrightarrow & x = \frac{-20}{441} & & \\ & V = \left\{ \frac{-20}{441} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -4x+\frac{5}{11} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -4x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-825}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{-220}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -825x \color{red}{+66} & = & \color{red}{-220x} +25 \\\Leftrightarrow & -825x \color{red}{+66} \color{blue}{-66} \color{blue}{+220x} & = & \color{red}{-220x} +25 \color{blue}{+220x} \color{blue}{-66} \\\Leftrightarrow & -825x+220x& = & 25-66 \\\Leftrightarrow & \color{red}{-605} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-605} & & \\\Leftrightarrow & x = \frac{41}{605} & & \\ & V = \left\{ \frac{41}{605} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{5})& = & -7x+\frac{5}{4} \\\Leftrightarrow & -16x-\frac{12}{5}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{-48} & = & \color{red}{-140x} +25 \\\Leftrightarrow & -320x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +25 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -320x+140x& = & 25+48 \\\Leftrightarrow & \color{red}{-180} x& = & 73 \\\Leftrightarrow & x = \frac{73}{-180} & & \\\Leftrightarrow & x = \frac{-73}{180} & & \\ & V = \left\{ \frac{-73}{180} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{3}{8})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 28x+\frac{21}{8}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{+21} & = & \color{red}{24x} +12 \\\Leftrightarrow & 224x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +12 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 224x-24x& = & 12-21 \\\Leftrightarrow & \color{red}{200} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{200} & & \\ & V = \left\{ \frac{-9}{200} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{8}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{+8} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 84x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & 84x+35x& = & 10-8 \\\Leftrightarrow & \color{red}{119} x& = & 2 \\\Leftrightarrow & x = \frac{2}{119} & & \\ & V = \left\{ \frac{2}{119} \right\} & \\\end{align}\)