Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{3}{5})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 12x-\frac{9}{5}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{81}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-81} & = & \color{red}{-225x} +35 \\\Leftrightarrow & 540x \color{red}{-81} \color{blue}{+81} \color{blue}{+225x} & = & \color{red}{-225x} +35 \color{blue}{+225x} \color{blue}{+81} \\\Leftrightarrow & 540x+225x& = & 35+81 \\\Leftrightarrow & \color{red}{765} x& = & 116 \\\Leftrightarrow & x = \frac{116}{765} & & \\ & V = \left\{ \frac{116}{765} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{3})& = & 3x+\frac{10}{9} \\\Leftrightarrow & 14x+\frac{35}{3}& = & 3x+\frac{10}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{105}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+105} & = & \color{red}{27x} +10 \\\Leftrightarrow & 126x \color{red}{+105} \color{blue}{-105} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{-105} \\\Leftrightarrow & 126x-27x& = & 10-105 \\\Leftrightarrow & \color{red}{99} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{99} & & \\ & V = \left\{ \frac{-95}{99} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{9})& = & 5x+\frac{3}{4} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{3}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{180}{ \color{blue}{36} }x+ \frac{27}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+32} & = & \color{red}{180x} +27 \\\Leftrightarrow & -432x \color{red}{+32} \color{blue}{-32} \color{blue}{-180x} & = & \color{red}{180x} +27 \color{blue}{-180x} \color{blue}{-32} \\\Leftrightarrow & -432x-180x& = & 27-32 \\\Leftrightarrow & \color{red}{-612} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-612} & & \\\Leftrightarrow & x = \frac{5}{612} & & \\ & V = \left\{ \frac{5}{612} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x+\frac{5}{2})& = & 9x+\frac{7}{9} \\\Leftrightarrow & 28x+\frac{35}{2}& = & 9x+\frac{7}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{504}{ \color{blue}{18} }x+ \frac{315}{ \color{blue}{18} })& = & (\frac{162}{ \color{blue}{18} }x+ \frac{14}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 504x \color{red}{+315} & = & \color{red}{162x} +14 \\\Leftrightarrow & 504x \color{red}{+315} \color{blue}{-315} \color{blue}{-162x} & = & \color{red}{162x} +14 \color{blue}{-162x} \color{blue}{-315} \\\Leftrightarrow & 504x-162x& = & 14-315 \\\Leftrightarrow & \color{red}{342} x& = & -301 \\\Leftrightarrow & x = \frac{-301}{342} & & \\ & V = \left\{ \frac{-301}{342} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{3})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 14x-\frac{14}{3}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{210}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 210x \color{red}{-70} & = & \color{red}{-75x} +24 \\\Leftrightarrow & 210x \color{red}{-70} \color{blue}{+70} \color{blue}{+75x} & = & \color{red}{-75x} +24 \color{blue}{+75x} \color{blue}{+70} \\\Leftrightarrow & 210x+75x& = & 24+70 \\\Leftrightarrow & \color{red}{285} x& = & 94 \\\Leftrightarrow & x = \frac{94}{285} & & \\ & V = \left\{ \frac{94}{285} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & -5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{396}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 396x \color{red}{-90} & = & \color{red}{-165x} +88 \\\Leftrightarrow & 396x \color{red}{-90} \color{blue}{+90} \color{blue}{+165x} & = & \color{red}{-165x} +88 \color{blue}{+165x} \color{blue}{+90} \\\Leftrightarrow & 396x+165x& = & 88+90 \\\Leftrightarrow & \color{red}{561} x& = & 178 \\\Leftrightarrow & x = \frac{178}{561} & & \\ & V = \left\{ \frac{178}{561} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{5})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 4x-\frac{6}{5}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{80}{ \color{blue}{20} }x- \frac{24}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 80x \color{red}{-24} & = & \color{red}{60x} +15 \\\Leftrightarrow & 80x \color{red}{-24} \color{blue}{+24} \color{blue}{-60x} & = & \color{red}{60x} +15 \color{blue}{-60x} \color{blue}{+24} \\\Leftrightarrow & 80x-60x& = & 15+24 \\\Leftrightarrow & \color{red}{20} x& = & 39 \\\Leftrightarrow & x = \frac{39}{20} & & \\ & V = \left\{ \frac{39}{20} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{3}{4})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -20x-\frac{15}{4}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{-252x} +16 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{+252x} & = & \color{red}{-252x} +16 \color{blue}{+252x} \color{blue}{+105} \\\Leftrightarrow & -560x+252x& = & 16+105 \\\Leftrightarrow & \color{red}{-308} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-308} & & \\\Leftrightarrow & x = \frac{-11}{28} & & \\ & V = \left\{ \frac{-11}{28} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{3}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{+12} \\\Leftrightarrow & 60x+25x& = & 6+12 \\\Leftrightarrow & \color{red}{85} x& = & 18 \\\Leftrightarrow & x = \frac{18}{85} & & \\ & V = \left\{ \frac{18}{85} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-108} & = & \color{red}{135x} +20 \\\Leftrightarrow & 900x \color{red}{-108} \color{blue}{+108} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{+108} \\\Leftrightarrow & 900x-135x& = & 20+108 \\\Leftrightarrow & \color{red}{765} x& = & 128 \\\Leftrightarrow & x = \frac{128}{765} & & \\ & V = \left\{ \frac{128}{765} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x-\frac{15}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-220}{ \color{blue}{22} }x- \frac{30}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -220x \color{red}{-30} & = & \color{red}{154x} +77 \\\Leftrightarrow & -220x \color{red}{-30} \color{blue}{+30} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{+30} \\\Leftrightarrow & -220x-154x& = & 77+30 \\\Leftrightarrow & \color{red}{-374} x& = & 107 \\\Leftrightarrow & x = \frac{107}{-374} & & \\\Leftrightarrow & x = \frac{-107}{374} & & \\ & V = \left\{ \frac{-107}{374} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 6x+\frac{8}{5} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 6x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-90}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{30}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -90x \color{red}{-12} & = & \color{red}{30x} +8 \\\Leftrightarrow & -90x \color{red}{-12} \color{blue}{+12} \color{blue}{-30x} & = & \color{red}{30x} +8 \color{blue}{-30x} \color{blue}{+12} \\\Leftrightarrow & -90x-30x& = & 8+12 \\\Leftrightarrow & \color{red}{-120} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-120} & & \\\Leftrightarrow & x = \frac{-1}{6} & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)