Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{9})& = & 5x+\frac{10}{9} \\\Leftrightarrow & 12x+\frac{8}{9}& = & 5x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+8} & = & \color{red}{45x} +10 \\\Leftrightarrow & 108x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +10 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 108x-45x& = & 10-8 \\\Leftrightarrow & \color{red}{63} x& = & 2 \\\Leftrightarrow & x = \frac{2}{63} & & \\ & V = \left\{ \frac{2}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1584}{ \color{blue}{132} }x- \frac{144}{ \color{blue}{132} })& = & (\frac{660}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1584x \color{red}{-144} & = & \color{red}{660x} +55 \\\Leftrightarrow & -1584x \color{red}{-144} \color{blue}{+144} \color{blue}{-660x} & = & \color{red}{660x} +55 \color{blue}{-660x} \color{blue}{+144} \\\Leftrightarrow & -1584x-660x& = & 55+144 \\\Leftrightarrow & \color{red}{-2244} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-2244} & & \\\Leftrightarrow & x = \frac{-199}{2244} & & \\ & V = \left\{ \frac{-199}{2244} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{9})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 10x-\frac{20}{9}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-20} & = & \color{red}{27x} +10 \\\Leftrightarrow & 90x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & 90x-27x& = & 10+20 \\\Leftrightarrow & \color{red}{63} x& = & 30 \\\Leftrightarrow & x = \frac{30}{63} & & \\\Leftrightarrow & x = \frac{10}{21} & & \\ & V = \left\{ \frac{10}{21} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -6x-\frac{10}{3}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x- \frac{100}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{-100} & = & \color{red}{210x} +21 \\\Leftrightarrow & -180x \color{red}{-100} \color{blue}{+100} \color{blue}{-210x} & = & \color{red}{210x} +21 \color{blue}{-210x} \color{blue}{+100} \\\Leftrightarrow & -180x-210x& = & 21+100 \\\Leftrightarrow & \color{red}{-390} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-390} & & \\\Leftrightarrow & x = \frac{-121}{390} & & \\ & V = \left\{ \frac{-121}{390} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & -2x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{300}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-40}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 300x \color{red}{-75} & = & \color{red}{-40x} +16 \\\Leftrightarrow & 300x \color{red}{-75} \color{blue}{+75} \color{blue}{+40x} & = & \color{red}{-40x} +16 \color{blue}{+40x} \color{blue}{+75} \\\Leftrightarrow & 300x+40x& = & 16+75 \\\Leftrightarrow & \color{red}{340} x& = & 91 \\\Leftrightarrow & x = \frac{91}{340} & & \\ & V = \left\{ \frac{91}{340} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{15}{4}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+165} & = & \color{red}{220x} +20 \\\Leftrightarrow & -528x \color{red}{+165} \color{blue}{-165} \color{blue}{-220x} & = & \color{red}{220x} +20 \color{blue}{-220x} \color{blue}{-165} \\\Leftrightarrow & -528x-220x& = & 20-165 \\\Leftrightarrow & \color{red}{-748} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-748} & & \\\Leftrightarrow & x = \frac{145}{748} & & \\ & V = \left\{ \frac{145}{748} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 6x-\frac{15}{4}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{120}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{6}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 120x \color{red}{-75} & = & \color{red}{-100x} +6 \\\Leftrightarrow & 120x \color{red}{-75} \color{blue}{+75} \color{blue}{+100x} & = & \color{red}{-100x} +6 \color{blue}{+100x} \color{blue}{+75} \\\Leftrightarrow & 120x+100x& = & 6+75 \\\Leftrightarrow & \color{red}{220} x& = & 81 \\\Leftrightarrow & x = \frac{81}{220} & & \\ & V = \left\{ \frac{81}{220} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{5})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{100}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{+48} & = & \color{red}{100x} +25 \\\Leftrightarrow & -240x \color{red}{+48} \color{blue}{-48} \color{blue}{-100x} & = & \color{red}{100x} +25 \color{blue}{-100x} \color{blue}{-48} \\\Leftrightarrow & -240x-100x& = & 25-48 \\\Leftrightarrow & \color{red}{-340} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-340} & & \\\Leftrightarrow & x = \frac{23}{340} & & \\ & V = \left\{ \frac{23}{340} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{11})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x+ \frac{63}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{+63} & = & \color{red}{-99x} +88 \\\Leftrightarrow & 462x \color{red}{+63} \color{blue}{-63} \color{blue}{+99x} & = & \color{red}{-99x} +88 \color{blue}{+99x} \color{blue}{-63} \\\Leftrightarrow & 462x+99x& = & 88-63 \\\Leftrightarrow & \color{red}{561} x& = & 25 \\\Leftrightarrow & x = \frac{25}{561} & & \\ & V = \left\{ \frac{25}{561} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{2}{5})& = & 9x+\frac{4}{7} \\\Leftrightarrow & -8x+\frac{8}{5}& = & 9x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+56} & = & \color{red}{315x} +20 \\\Leftrightarrow & -280x \color{red}{+56} \color{blue}{-56} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{-56} \\\Leftrightarrow & -280x-315x& = & 20-56 \\\Leftrightarrow & \color{red}{-595} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-595} & & \\\Leftrightarrow & x = \frac{36}{595} & & \\ & V = \left\{ \frac{36}{595} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{11})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -20x-\frac{20}{11}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x- \frac{200}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{-200} & = & \color{red}{-990x} +99 \\\Leftrightarrow & -2200x \color{red}{-200} \color{blue}{+200} \color{blue}{+990x} & = & \color{red}{-990x} +99 \color{blue}{+990x} \color{blue}{+200} \\\Leftrightarrow & -2200x+990x& = & 99+200 \\\Leftrightarrow & \color{red}{-1210} x& = & 299 \\\Leftrightarrow & x = \frac{299}{-1210} & & \\\Leftrightarrow & x = \frac{-299}{1210} & & \\ & V = \left\{ \frac{-299}{1210} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{11})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -8x-\frac{4}{11}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x- \frac{36}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{-36} & = & \color{red}{-297x} +110 \\\Leftrightarrow & -792x \color{red}{-36} \color{blue}{+36} \color{blue}{+297x} & = & \color{red}{-297x} +110 \color{blue}{+297x} \color{blue}{+36} \\\Leftrightarrow & -792x+297x& = & 110+36 \\\Leftrightarrow & \color{red}{-495} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-495} & & \\\Leftrightarrow & x = \frac{-146}{495} & & \\ & V = \left\{ \frac{-146}{495} \right\} & \\\end{align}\)