Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{5}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 16x+\frac{20}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{+20} & = & \color{red}{45x} +6 \\\Leftrightarrow & 144x \color{red}{+20} \color{blue}{-20} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-20} \\\Leftrightarrow & 144x-45x& = & 6-20 \\\Leftrightarrow & \color{red}{99} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{99} & & \\ & V = \left\{ \frac{-14}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{2}{7})& = & 3x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{10}{7}& = & 3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-110} & = & \color{red}{231x} +42 \\\Leftrightarrow & 1540x \color{red}{-110} \color{blue}{+110} \color{blue}{-231x} & = & \color{red}{231x} +42 \color{blue}{-231x} \color{blue}{+110} \\\Leftrightarrow & 1540x-231x& = & 42+110 \\\Leftrightarrow & \color{red}{1309} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1309} & & \\ & V = \left\{ \frac{152}{1309} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{24}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{120}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-120} & = & \color{red}{315x} +42 \\\Leftrightarrow & -630x \color{red}{-120} \color{blue}{+120} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+120} \\\Leftrightarrow & -630x-315x& = & 42+120 \\\Leftrightarrow & \color{red}{-945} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-945} & & \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{-18} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & -132x+55x& = & 2+18 \\\Leftrightarrow & \color{red}{-77} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-77} & & \\\Leftrightarrow & x = \frac{-20}{77} & & \\ & V = \left\{ \frac{-20}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{20}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{2200}{ \color{blue}{110} }x+ \frac{200}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 2200x \color{red}{+200} & = & \color{red}{-330x} +99 \\\Leftrightarrow & 2200x \color{red}{+200} \color{blue}{-200} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{-200} \\\Leftrightarrow & 2200x+330x& = & 99-200 \\\Leftrightarrow & \color{red}{2530} x& = & -101 \\\Leftrightarrow & x = \frac{-101}{2530} & & \\ & V = \left\{ \frac{-101}{2530} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{2}{9})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 28x+\frac{14}{9}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2772}{ \color{blue}{99} }x+ \frac{154}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2772x \color{red}{+154} & = & \color{red}{891x} +90 \\\Leftrightarrow & 2772x \color{red}{+154} \color{blue}{-154} \color{blue}{-891x} & = & \color{red}{891x} +90 \color{blue}{-891x} \color{blue}{-154} \\\Leftrightarrow & 2772x-891x& = & 90-154 \\\Leftrightarrow & \color{red}{1881} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{1881} & & \\ & V = \left\{ \frac{-64}{1881} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{126}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-126} & = & \color{red}{539x} +88 \\\Leftrightarrow & 2310x \color{red}{-126} \color{blue}{+126} \color{blue}{-539x} & = & \color{red}{539x} +88 \color{blue}{-539x} \color{blue}{+126} \\\Leftrightarrow & 2310x-539x& = & 88+126 \\\Leftrightarrow & \color{red}{1771} x& = & 214 \\\Leftrightarrow & x = \frac{214}{1771} & & \\ & V = \left\{ \frac{214}{1771} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{5}{9})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 14x+\frac{35}{9}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{-495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{+385} & = & \color{red}{-495x} +45 \\\Leftrightarrow & 1386x \color{red}{+385} \color{blue}{-385} \color{blue}{+495x} & = & \color{red}{-495x} +45 \color{blue}{+495x} \color{blue}{-385} \\\Leftrightarrow & 1386x+495x& = & 45-385 \\\Leftrightarrow & \color{red}{1881} x& = & -340 \\\Leftrightarrow & x = \frac{-340}{1881} & & \\ & V = \left\{ \frac{-340}{1881} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{3}{11})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -30x+\frac{18}{11}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{+18} & = & \color{red}{-77x} +3 \\\Leftrightarrow & -330x \color{red}{+18} \color{blue}{-18} \color{blue}{+77x} & = & \color{red}{-77x} +3 \color{blue}{+77x} \color{blue}{-18} \\\Leftrightarrow & -330x+77x& = & 3-18 \\\Leftrightarrow & \color{red}{-253} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-253} & & \\\Leftrightarrow & x = \frac{15}{253} & & \\ & V = \left\{ \frac{15}{253} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+20} & = & \color{red}{-98x} +63 \\\Leftrightarrow & -84x \color{red}{+20} \color{blue}{-20} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{-20} \\\Leftrightarrow & -84x+98x& = & 63-20 \\\Leftrightarrow & \color{red}{14} x& = & 43 \\\Leftrightarrow & x = \frac{43}{14} & & \\ & V = \left\{ \frac{43}{14} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{3}{4})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 10x+\frac{15}{4}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+45} & = & \color{red}{-108x} +16 \\\Leftrightarrow & 120x \color{red}{+45} \color{blue}{-45} \color{blue}{+108x} & = & \color{red}{-108x} +16 \color{blue}{+108x} \color{blue}{-45} \\\Leftrightarrow & 120x+108x& = & 16-45 \\\Leftrightarrow & \color{red}{228} x& = & -29 \\\Leftrightarrow & x = \frac{-29}{228} & & \\ & V = \left\{ \frac{-29}{228} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{3}{11})& = & -9x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{12}{11}& = & -9x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1980}{ \color{blue}{99} }x+ \frac{108}{ \color{blue}{99} })& = & (\frac{-891}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1980x \color{red}{+108} & = & \color{red}{-891x} +22 \\\Leftrightarrow & 1980x \color{red}{+108} \color{blue}{-108} \color{blue}{+891x} & = & \color{red}{-891x} +22 \color{blue}{+891x} \color{blue}{-108} \\\Leftrightarrow & 1980x+891x& = & 22-108 \\\Leftrightarrow & \color{red}{2871} x& = & -86 \\\Leftrightarrow & x = \frac{-86}{2871} & & \\ & V = \left\{ \frac{-86}{2871} \right\} & \\\end{align}\)