Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{9})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 12x+\frac{20}{9}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1188}{ \color{blue}{99} }x+ \frac{220}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{45}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1188x \color{red}{+220} & = & \color{red}{495x} +45 \\\Leftrightarrow & 1188x \color{red}{+220} \color{blue}{-220} \color{blue}{-495x} & = & \color{red}{495x} +45 \color{blue}{-495x} \color{blue}{-220} \\\Leftrightarrow & 1188x-495x& = & 45-220 \\\Leftrightarrow & \color{red}{693} x& = & -175 \\\Leftrightarrow & x = \frac{-175}{693} & & \\\Leftrightarrow & x = \frac{-25}{99} & & \\ & V = \left\{ \frac{-25}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & 5x+\frac{7}{10} \\\Leftrightarrow & 16x-\frac{8}{9}& = & 5x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1440}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{450}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1440x \color{red}{-80} & = & \color{red}{450x} +63 \\\Leftrightarrow & 1440x \color{red}{-80} \color{blue}{+80} \color{blue}{-450x} & = & \color{red}{450x} +63 \color{blue}{-450x} \color{blue}{+80} \\\Leftrightarrow & 1440x-450x& = & 63+80 \\\Leftrightarrow & \color{red}{990} x& = & 143 \\\Leftrightarrow & x = \frac{143}{990} & & \\\Leftrightarrow & x = \frac{13}{90} & & \\ & V = \left\{ \frac{13}{90} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & 2x+\frac{7}{12} \\\Leftrightarrow & 9x+\frac{15}{7}& = & 2x+\frac{7}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{756}{ \color{blue}{84} }x+ \frac{180}{ \color{blue}{84} })& = & (\frac{168}{ \color{blue}{84} }x+ \frac{49}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 756x \color{red}{+180} & = & \color{red}{168x} +49 \\\Leftrightarrow & 756x \color{red}{+180} \color{blue}{-180} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{-180} \\\Leftrightarrow & 756x-168x& = & 49-180 \\\Leftrightarrow & \color{red}{588} x& = & -131 \\\Leftrightarrow & x = \frac{-131}{588} & & \\ & V = \left\{ \frac{-131}{588} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{11})& = & 7x+\frac{10}{3} \\\Leftrightarrow & -20x-\frac{8}{11}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x- \frac{24}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{-24} & = & \color{red}{231x} +110 \\\Leftrightarrow & -660x \color{red}{-24} \color{blue}{+24} \color{blue}{-231x} & = & \color{red}{231x} +110 \color{blue}{-231x} \color{blue}{+24} \\\Leftrightarrow & -660x-231x& = & 110+24 \\\Leftrightarrow & \color{red}{-891} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-891} & & \\\Leftrightarrow & x = \frac{-134}{891} & & \\ & V = \left\{ \frac{-134}{891} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{9})& = & -9x+\frac{5}{4} \\\Leftrightarrow & 4x+\frac{8}{9}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{144}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-324}{ \color{blue}{36} }x+ \frac{45}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 144x \color{red}{+32} & = & \color{red}{-324x} +45 \\\Leftrightarrow & 144x \color{red}{+32} \color{blue}{-32} \color{blue}{+324x} & = & \color{red}{-324x} +45 \color{blue}{+324x} \color{blue}{-32} \\\Leftrightarrow & 144x+324x& = & 45-32 \\\Leftrightarrow & \color{red}{468} x& = & 13 \\\Leftrightarrow & x = \frac{13}{468} & & \\\Leftrightarrow & x = \frac{1}{36} & & \\ & V = \left\{ \frac{1}{36} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{4}{9})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -35x-\frac{28}{9}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -3465x \color{red}{-308} & = & \color{red}{-297x} +54 \\\Leftrightarrow & -3465x \color{red}{-308} \color{blue}{+308} \color{blue}{+297x} & = & \color{red}{-297x} +54 \color{blue}{+297x} \color{blue}{+308} \\\Leftrightarrow & -3465x+297x& = & 54+308 \\\Leftrightarrow & \color{red}{-3168} x& = & 362 \\\Leftrightarrow & x = \frac{362}{-3168} & & \\\Leftrightarrow & x = \frac{-181}{1584} & & \\ & V = \left\{ \frac{-181}{1584} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{63x} +28 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-18} \\\Leftrightarrow & 168x-63x& = & 28-18 \\\Leftrightarrow & \color{red}{105} x& = & 10 \\\Leftrightarrow & x = \frac{10}{105} & & \\\Leftrightarrow & x = \frac{2}{21} & & \\ & V = \left\{ \frac{2}{21} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{5})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{275x} +35 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +35 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & 660x-275x& = & 35+132 \\\Leftrightarrow & \color{red}{385} x& = & 167 \\\Leftrightarrow & x = \frac{167}{385} & & \\ & V = \left\{ \frac{167}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{11})& = & 5x+\frac{3}{2} \\\Leftrightarrow & -14x+\frac{21}{11}& = & 5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x+ \frac{42}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{+42} & = & \color{red}{110x} +33 \\\Leftrightarrow & -308x \color{red}{+42} \color{blue}{-42} \color{blue}{-110x} & = & \color{red}{110x} +33 \color{blue}{-110x} \color{blue}{-42} \\\Leftrightarrow & -308x-110x& = & 33-42 \\\Leftrightarrow & \color{red}{-418} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-418} & & \\\Leftrightarrow & x = \frac{9}{418} & & \\ & V = \left\{ \frac{9}{418} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{11})& = & 9x+\frac{3}{11} \\\Leftrightarrow & 28x+\frac{35}{11}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{308}{ \color{blue}{11} }x+ \frac{35}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 308x \color{red}{+35} & = & \color{red}{99x} +3 \\\Leftrightarrow & 308x \color{red}{+35} \color{blue}{-35} \color{blue}{-99x} & = & \color{red}{99x} +3 \color{blue}{-99x} \color{blue}{-35} \\\Leftrightarrow & 308x-99x& = & 3-35 \\\Leftrightarrow & \color{red}{209} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{209} & & \\ & V = \left\{ \frac{-32}{209} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -20x+\frac{20}{3}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-660}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -660x \color{red}{+220} & = & \color{red}{231x} +24 \\\Leftrightarrow & -660x \color{red}{+220} \color{blue}{-220} \color{blue}{-231x} & = & \color{red}{231x} +24 \color{blue}{-231x} \color{blue}{-220} \\\Leftrightarrow & -660x-231x& = & 24-220 \\\Leftrightarrow & \color{red}{-891} x& = & -196 \\\Leftrightarrow & x = \frac{-196}{-891} & & \\\Leftrightarrow & x = \frac{196}{891} & & \\ & V = \left\{ \frac{196}{891} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{11})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 14x+\frac{14}{11}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{616}{ \color{blue}{44} }x+ \frac{56}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 616x \color{red}{+56} & = & \color{red}{-132x} +99 \\\Leftrightarrow & 616x \color{red}{+56} \color{blue}{-56} \color{blue}{+132x} & = & \color{red}{-132x} +99 \color{blue}{+132x} \color{blue}{-56} \\\Leftrightarrow & 616x+132x& = & 99-56 \\\Leftrightarrow & \color{red}{748} x& = & 43 \\\Leftrightarrow & x = \frac{43}{748} & & \\ & V = \left\{ \frac{43}{748} \right\} & \\\end{align}\)