Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{4}{9})& = & -9x+\frac{6}{5} \\\Leftrightarrow & -4x-\frac{8}{9}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{-40} & = & \color{red}{-405x} +54 \\\Leftrightarrow & -180x \color{red}{-40} \color{blue}{+40} \color{blue}{+405x} & = & \color{red}{-405x} +54 \color{blue}{+405x} \color{blue}{+40} \\\Leftrightarrow & -180x+405x& = & 54+40 \\\Leftrightarrow & \color{red}{225} x& = & 94 \\\Leftrightarrow & x = \frac{94}{225} & & \\ & V = \left\{ \frac{94}{225} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{4}{11})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 8x+\frac{16}{11}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{264}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 264x \color{red}{+48} & = & \color{red}{99x} +44 \\\Leftrightarrow & 264x \color{red}{+48} \color{blue}{-48} \color{blue}{-99x} & = & \color{red}{99x} +44 \color{blue}{-99x} \color{blue}{-48} \\\Leftrightarrow & 264x-99x& = & 44-48 \\\Leftrightarrow & \color{red}{165} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{165} & & \\ & V = \left\{ \frac{-4}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{2}{3})& = & -6x+\frac{7}{5} \\\Leftrightarrow & -28x-\frac{14}{3}& = & -6x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-420}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-90}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -420x \color{red}{-70} & = & \color{red}{-90x} +21 \\\Leftrightarrow & -420x \color{red}{-70} \color{blue}{+70} \color{blue}{+90x} & = & \color{red}{-90x} +21 \color{blue}{+90x} \color{blue}{+70} \\\Leftrightarrow & -420x+90x& = & 21+70 \\\Leftrightarrow & \color{red}{-330} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-330} & & \\\Leftrightarrow & x = \frac{-91}{330} & & \\ & V = \left\{ \frac{-91}{330} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{2}{11})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -24x+\frac{12}{11}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{+84} & = & \color{red}{385x} +44 \\\Leftrightarrow & -1848x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +44 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & -1848x-385x& = & 44-84 \\\Leftrightarrow & \color{red}{-2233} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{-2233} & & \\\Leftrightarrow & x = \frac{40}{2233} & & \\ & V = \left\{ \frac{40}{2233} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{5})& = & -8x+\frac{8}{9} \\\Leftrightarrow & -15x-\frac{9}{5}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-81} & = & \color{red}{-360x} +40 \\\Leftrightarrow & -675x \color{red}{-81} \color{blue}{+81} \color{blue}{+360x} & = & \color{red}{-360x} +40 \color{blue}{+360x} \color{blue}{+81} \\\Leftrightarrow & -675x+360x& = & 40+81 \\\Leftrightarrow & \color{red}{-315} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-315} & & \\\Leftrightarrow & x = \frac{-121}{315} & & \\ & V = \left\{ \frac{-121}{315} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{8})& = & -9x+\frac{2}{11} \\\Leftrightarrow & -25x-\frac{15}{8}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x- \frac{165}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{16}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{-165} & = & \color{red}{-792x} +16 \\\Leftrightarrow & -2200x \color{red}{-165} \color{blue}{+165} \color{blue}{+792x} & = & \color{red}{-792x} +16 \color{blue}{+792x} \color{blue}{+165} \\\Leftrightarrow & -2200x+792x& = & 16+165 \\\Leftrightarrow & \color{red}{-1408} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-1408} & & \\\Leftrightarrow & x = \frac{-181}{1408} & & \\ & V = \left\{ \frac{-181}{1408} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{2}{7})& = & 7x+\frac{9}{4} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-168}{ \color{blue}{28} }x+ \frac{24}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{196x} +63 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{-196x} & = & \color{red}{196x} +63 \color{blue}{-196x} \color{blue}{-24} \\\Leftrightarrow & -168x-196x& = & 63-24 \\\Leftrightarrow & \color{red}{-364} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-364} & & \\\Leftrightarrow & x = \frac{-3}{28} & & \\ & V = \left\{ \frac{-3}{28} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{9})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x+\frac{8}{9}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+56} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 756x \color{red}{+56} \color{blue}{-56} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-56} \\\Leftrightarrow & 756x+315x& = & 54-56 \\\Leftrightarrow & \color{red}{1071} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{1071} & & \\ & V = \left\{ \frac{-2}{1071} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & -84x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & -84x+105x& = & 70+18 \\\Leftrightarrow & \color{red}{21} x& = & 88 \\\Leftrightarrow & x = \frac{88}{21} & & \\ & V = \left\{ \frac{88}{21} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{3})& = & 8x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{20}{3}& = & 8x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{24}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{-20} & = & \color{red}{24x} +2 \\\Leftrightarrow & -45x \color{red}{-20} \color{blue}{+20} \color{blue}{-24x} & = & \color{red}{24x} +2 \color{blue}{-24x} \color{blue}{+20} \\\Leftrightarrow & -45x-24x& = & 2+20 \\\Leftrightarrow & \color{red}{-69} x& = & 22 \\\Leftrightarrow & x = \frac{22}{-69} & & \\\Leftrightarrow & x = \frac{-22}{69} & & \\ & V = \left\{ \frac{-22}{69} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{7})& = & 9x+\frac{3}{11} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{-220} & = & \color{red}{693x} +21 \\\Leftrightarrow & 1540x \color{red}{-220} \color{blue}{+220} \color{blue}{-693x} & = & \color{red}{693x} +21 \color{blue}{-693x} \color{blue}{+220} \\\Leftrightarrow & 1540x-693x& = & 21+220 \\\Leftrightarrow & \color{red}{847} x& = & 241 \\\Leftrightarrow & x = \frac{241}{847} & & \\ & V = \left\{ \frac{241}{847} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{5})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{9}{5}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+27} & = & \color{red}{105x} +50 \\\Leftrightarrow & 225x \color{red}{+27} \color{blue}{-27} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-27} \\\Leftrightarrow & 225x-105x& = & 50-27 \\\Leftrightarrow & \color{red}{120} x& = & 23 \\\Leftrightarrow & x = \frac{23}{120} & & \\ & V = \left\{ \frac{23}{120} \right\} & \\\end{align}\)