Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{15}{4}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{440}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{40}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 440x \color{red}{-165} & = & \color{red}{-396x} +40 \\\Leftrightarrow & 440x \color{red}{-165} \color{blue}{+165} \color{blue}{+396x} & = & \color{red}{-396x} +40 \color{blue}{+396x} \color{blue}{+165} \\\Leftrightarrow & 440x+396x& = & 40+165 \\\Leftrightarrow & \color{red}{836} x& = & 205 \\\Leftrightarrow & x = \frac{205}{836} & & \\ & V = \left\{ \frac{205}{836} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{4}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 12x-\frac{24}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{216}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-216} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 540x \color{red}{-216} \color{blue}{+216} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+216} \\\Leftrightarrow & 540x+225x& = & 25+216 \\\Leftrightarrow & \color{red}{765} x& = & 241 \\\Leftrightarrow & x = \frac{241}{765} & & \\ & V = \left\{ \frac{241}{765} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{8})& = & 7x+\frac{7}{6} \\\Leftrightarrow & 15x-\frac{15}{8}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 8 en 6 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{360}{ \color{blue}{24} }x- \frac{45}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{28}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 360x \color{red}{-45} & = & \color{red}{168x} +28 \\\Leftrightarrow & 360x \color{red}{-45} \color{blue}{+45} \color{blue}{-168x} & = & \color{red}{168x} +28 \color{blue}{-168x} \color{blue}{+45} \\\Leftrightarrow & 360x-168x& = & 28+45 \\\Leftrightarrow & \color{red}{192} x& = & 73 \\\Leftrightarrow & x = \frac{73}{192} & & \\ & V = \left\{ \frac{73}{192} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{9})& = & 7x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{8}{9}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-56} & = & \color{red}{441x} +81 \\\Leftrightarrow & 756x \color{red}{-56} \color{blue}{+56} \color{blue}{-441x} & = & \color{red}{441x} +81 \color{blue}{-441x} \color{blue}{+56} \\\Leftrightarrow & 756x-441x& = & 81+56 \\\Leftrightarrow & \color{red}{315} x& = & 137 \\\Leftrightarrow & x = \frac{137}{315} & & \\ & V = \left\{ \frac{137}{315} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{3}{11})& = & 7x+\frac{4}{3} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+54} & = & \color{red}{231x} +44 \\\Leftrightarrow & -792x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & -792x-231x& = & 44-54 \\\Leftrightarrow & \color{red}{-1023} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-1023} & & \\\Leftrightarrow & x = \frac{10}{1023} & & \\ & V = \left\{ \frac{10}{1023} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{24}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{297x} +24 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{-297x} & = & \color{red}{297x} +24 \color{blue}{-297x} \color{blue}{-220} \\\Leftrightarrow & -264x-297x& = & 24-220 \\\Leftrightarrow & \color{red}{-561} x& = & -196 \\\Leftrightarrow & x = \frac{-196}{-561} & & \\\Leftrightarrow & x = \frac{196}{561} & & \\ & V = \left\{ \frac{196}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{9})& = & 8x+\frac{6}{7} \\\Leftrightarrow & -21x+\frac{28}{9}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1323}{ \color{blue}{63} }x+ \frac{196}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1323x \color{red}{+196} & = & \color{red}{504x} +54 \\\Leftrightarrow & -1323x \color{red}{+196} \color{blue}{-196} \color{blue}{-504x} & = & \color{red}{504x} +54 \color{blue}{-504x} \color{blue}{-196} \\\Leftrightarrow & -1323x-504x& = & 54-196 \\\Leftrightarrow & \color{red}{-1827} x& = & -142 \\\Leftrightarrow & x = \frac{-142}{-1827} & & \\\Leftrightarrow & x = \frac{142}{1827} & & \\ & V = \left\{ \frac{142}{1827} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -7x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{675}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 675x \color{red}{+54} & = & \color{red}{-315x} +40 \\\Leftrightarrow & 675x \color{red}{+54} \color{blue}{-54} \color{blue}{+315x} & = & \color{red}{-315x} +40 \color{blue}{+315x} \color{blue}{-54} \\\Leftrightarrow & 675x+315x& = & 40-54 \\\Leftrightarrow & \color{red}{990} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{990} & & \\\Leftrightarrow & x = \frac{-7}{495} & & \\ & V = \left\{ \frac{-7}{495} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{3})& = & 3x+\frac{8}{5} \\\Leftrightarrow & 20x+\frac{8}{3}& = & 3x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+40} & = & \color{red}{45x} +24 \\\Leftrightarrow & 300x \color{red}{+40} \color{blue}{-40} \color{blue}{-45x} & = & \color{red}{45x} +24 \color{blue}{-45x} \color{blue}{-40} \\\Leftrightarrow & 300x-45x& = & 24-40 \\\Leftrightarrow & \color{red}{255} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{255} & & \\ & V = \left\{ \frac{-16}{255} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{3}{7})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{6}{7}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+6} & = & \color{red}{-49x} +6 \\\Leftrightarrow & -70x \color{red}{+6} \color{blue}{-6} \color{blue}{+49x} & = & \color{red}{-49x} +6 \color{blue}{+49x} \color{blue}{-6} \\\Leftrightarrow & -70x+49x& = & 6-6 \\\Leftrightarrow & \color{red}{-21} x& = & 0 \\\Leftrightarrow & x = \frac{0}{-21} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{3})& = & 9x+\frac{5}{6} \\\Leftrightarrow & 14x+\frac{14}{3}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{28}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+28} & = & \color{red}{54x} +5 \\\Leftrightarrow & 84x \color{red}{+28} \color{blue}{-28} \color{blue}{-54x} & = & \color{red}{54x} +5 \color{blue}{-54x} \color{blue}{-28} \\\Leftrightarrow & 84x-54x& = & 5-28 \\\Leftrightarrow & \color{red}{30} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{30} & & \\ & V = \left\{ \frac{-23}{30} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & -9x+\frac{4}{9} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -9x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-567x} +28 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +28 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & 252x+567x& = & 28-90 \\\Leftrightarrow & \color{red}{819} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{819} & & \\ & V = \left\{ \frac{-62}{819} \right\} & \\\end{align}\)