Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{3}{10})& = & -2x+\frac{9}{5} \\\Leftrightarrow & 15x-\frac{9}{10}& = & -2x+\frac{9}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{-20}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-9} & = & \color{red}{-20x} +18 \\\Leftrightarrow & 150x \color{red}{-9} \color{blue}{+9} \color{blue}{+20x} & = & \color{red}{-20x} +18 \color{blue}{+20x} \color{blue}{+9} \\\Leftrightarrow & 150x+20x& = & 18+9 \\\Leftrightarrow & \color{red}{170} x& = & 27 \\\Leftrightarrow & x = \frac{27}{170} & & \\ & V = \left\{ \frac{27}{170} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{3}{8})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 21x+\frac{21}{8}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{504}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{-96}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 504x \color{red}{+63} & = & \color{red}{-96x} +64 \\\Leftrightarrow & 504x \color{red}{+63} \color{blue}{-63} \color{blue}{+96x} & = & \color{red}{-96x} +64 \color{blue}{+96x} \color{blue}{-63} \\\Leftrightarrow & 504x+96x& = & 64-63 \\\Leftrightarrow & \color{red}{600} x& = & 1 \\\Leftrightarrow & x = \frac{1}{600} & & \\ & V = \left\{ \frac{1}{600} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{2})& = & -6x+\frac{8}{5} \\\Leftrightarrow & -28x+\frac{21}{2}& = & -6x+\frac{8}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x+ \frac{105}{ \color{blue}{10} })& = & (\frac{-60}{ \color{blue}{10} }x+ \frac{16}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{+105} & = & \color{red}{-60x} +16 \\\Leftrightarrow & -280x \color{red}{+105} \color{blue}{-105} \color{blue}{+60x} & = & \color{red}{-60x} +16 \color{blue}{+60x} \color{blue}{-105} \\\Leftrightarrow & -280x+60x& = & 16-105 \\\Leftrightarrow & \color{red}{-220} x& = & -89 \\\Leftrightarrow & x = \frac{-89}{-220} & & \\\Leftrightarrow & x = \frac{89}{220} & & \\ & V = \left\{ \frac{89}{220} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{10}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+50} & = & \color{red}{105x} +18 \\\Leftrightarrow & 120x \color{red}{+50} \color{blue}{-50} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-50} \\\Leftrightarrow & 120x-105x& = & 18-50 \\\Leftrightarrow & \color{red}{15} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{15} & & \\ & V = \left\{ \frac{-32}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{4}{9})& = & -4x+\frac{3}{10} \\\Leftrightarrow & -25x+\frac{20}{9}& = & -4x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-2250}{ \color{blue}{90} }x+ \frac{200}{ \color{blue}{90} })& = & (\frac{-360}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -2250x \color{red}{+200} & = & \color{red}{-360x} +27 \\\Leftrightarrow & -2250x \color{red}{+200} \color{blue}{-200} \color{blue}{+360x} & = & \color{red}{-360x} +27 \color{blue}{+360x} \color{blue}{-200} \\\Leftrightarrow & -2250x+360x& = & 27-200 \\\Leftrightarrow & \color{red}{-1890} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{-1890} & & \\\Leftrightarrow & x = \frac{173}{1890} & & \\ & V = \left\{ \frac{173}{1890} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{5}{6})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -10x+\frac{25}{6}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 6 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x+ \frac{125}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{+125} & = & \color{red}{210x} +27 \\\Leftrightarrow & -300x \color{red}{+125} \color{blue}{-125} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{-125} \\\Leftrightarrow & -300x-210x& = & 27-125 \\\Leftrightarrow & \color{red}{-510} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-510} & & \\\Leftrightarrow & x = \frac{49}{255} & & \\ & V = \left\{ \frac{49}{255} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{9})& = & 4x+\frac{5}{7} \\\Leftrightarrow & -15x+\frac{20}{9}& = & 4x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{140}{ \color{blue}{63} })& = & (\frac{252}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+140} & = & \color{red}{252x} +45 \\\Leftrightarrow & -945x \color{red}{+140} \color{blue}{-140} \color{blue}{-252x} & = & \color{red}{252x} +45 \color{blue}{-252x} \color{blue}{-140} \\\Leftrightarrow & -945x-252x& = & 45-140 \\\Leftrightarrow & \color{red}{-1197} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-1197} & & \\\Leftrightarrow & x = \frac{5}{63} & & \\ & V = \left\{ \frac{5}{63} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{5})& = & 8x+\frac{5}{12} \\\Leftrightarrow & 21x+\frac{28}{5}& = & 8x+\frac{5}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{1260}{ \color{blue}{60} }x+ \frac{336}{ \color{blue}{60} })& = & (\frac{480}{ \color{blue}{60} }x+ \frac{25}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 1260x \color{red}{+336} & = & \color{red}{480x} +25 \\\Leftrightarrow & 1260x \color{red}{+336} \color{blue}{-336} \color{blue}{-480x} & = & \color{red}{480x} +25 \color{blue}{-480x} \color{blue}{-336} \\\Leftrightarrow & 1260x-480x& = & 25-336 \\\Leftrightarrow & \color{red}{780} x& = & -311 \\\Leftrightarrow & x = \frac{-311}{780} & & \\ & V = \left\{ \frac{-311}{780} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -24x+\frac{18}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-336}{ \color{blue}{14} }x+ \frac{36}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -336x \color{red}{+36} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -336x \color{red}{+36} \color{blue}{-36} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-36} \\\Leftrightarrow & -336x+70x& = & 35-36 \\\Leftrightarrow & \color{red}{-266} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{-266} & & \\\Leftrightarrow & x = \frac{1}{266} & & \\ & V = \left\{ \frac{1}{266} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{10})& = & -5x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{9}{10}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{70}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-99} & = & \color{red}{-550x} +70 \\\Leftrightarrow & 1320x \color{red}{-99} \color{blue}{+99} \color{blue}{+550x} & = & \color{red}{-550x} +70 \color{blue}{+550x} \color{blue}{+99} \\\Leftrightarrow & 1320x+550x& = & 70+99 \\\Leftrightarrow & \color{red}{1870} x& = & 169 \\\Leftrightarrow & x = \frac{169}{1870} & & \\ & V = \left\{ \frac{169}{1870} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{4}{5})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{12}{5}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{+132} & = & \color{red}{-385x} +50 \\\Leftrightarrow & 825x \color{red}{+132} \color{blue}{-132} \color{blue}{+385x} & = & \color{red}{-385x} +50 \color{blue}{+385x} \color{blue}{-132} \\\Leftrightarrow & 825x+385x& = & 50-132 \\\Leftrightarrow & \color{red}{1210} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{1210} & & \\\Leftrightarrow & x = \frac{-41}{605} & & \\ & V = \left\{ \frac{-41}{605} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1260}{ \color{blue}{42} }x+ \frac{180}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1260x \color{red}{+180} & = & \color{red}{-294x} +35 \\\Leftrightarrow & -1260x \color{red}{+180} \color{blue}{-180} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{-180} \\\Leftrightarrow & -1260x+294x& = & 35-180 \\\Leftrightarrow & \color{red}{-966} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-966} & & \\\Leftrightarrow & x = \frac{145}{966} & & \\ & V = \left\{ \frac{145}{966} \right\} & \\\end{align}\)