Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{3}{7})& = & -7x+\frac{9}{5} \\\Leftrightarrow & 4x-\frac{6}{7}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-30} & = & \color{red}{-245x} +63 \\\Leftrightarrow & 140x \color{red}{-30} \color{blue}{+30} \color{blue}{+245x} & = & \color{red}{-245x} +63 \color{blue}{+245x} \color{blue}{+30} \\\Leftrightarrow & 140x+245x& = & 63+30 \\\Leftrightarrow & \color{red}{385} x& = & 93 \\\Leftrightarrow & x = \frac{93}{385} & & \\ & V = \left\{ \frac{93}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -9x-\frac{15}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x- \frac{30}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{-30} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -126x \color{red}{-30} \color{blue}{+30} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+30} \\\Leftrightarrow & -126x+70x& = & 63+30 \\\Leftrightarrow & \color{red}{-56} x& = & 93 \\\Leftrightarrow & x = \frac{93}{-56} & & \\\Leftrightarrow & x = \frac{-93}{56} & & \\ & V = \left\{ \frac{-93}{56} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x-\frac{4}{9})& = & -8x+\frac{3}{11} \\\Leftrightarrow & 35x-\frac{28}{9}& = & -8x+\frac{3}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{3465}{ \color{blue}{99} }x- \frac{308}{ \color{blue}{99} })& = & (\frac{-792}{ \color{blue}{99} }x+ \frac{27}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 3465x \color{red}{-308} & = & \color{red}{-792x} +27 \\\Leftrightarrow & 3465x \color{red}{-308} \color{blue}{+308} \color{blue}{+792x} & = & \color{red}{-792x} +27 \color{blue}{+792x} \color{blue}{+308} \\\Leftrightarrow & 3465x+792x& = & 27+308 \\\Leftrightarrow & \color{red}{4257} x& = & 335 \\\Leftrightarrow & x = \frac{335}{4257} & & \\ & V = \left\{ \frac{335}{4257} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x- \frac{44}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{-44} & = & \color{red}{-693x} +36 \\\Leftrightarrow & 594x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +36 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & 594x+693x& = & 36+44 \\\Leftrightarrow & \color{red}{1287} x& = & 80 \\\Leftrightarrow & x = \frac{80}{1287} & & \\ & V = \left\{ \frac{80}{1287} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{5})& = & -8x+\frac{5}{2} \\\Leftrightarrow & 21x-\frac{14}{5}& = & -8x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{28}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-28} & = & \color{red}{-80x} +25 \\\Leftrightarrow & 210x \color{red}{-28} \color{blue}{+28} \color{blue}{+80x} & = & \color{red}{-80x} +25 \color{blue}{+80x} \color{blue}{+28} \\\Leftrightarrow & 210x+80x& = & 25+28 \\\Leftrightarrow & \color{red}{290} x& = & 53 \\\Leftrightarrow & x = \frac{53}{290} & & \\ & V = \left\{ \frac{53}{290} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{2}{11})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x+\frac{8}{11}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+8} & = & \color{red}{-55x} +10 \\\Leftrightarrow & -132x \color{red}{+8} \color{blue}{-8} \color{blue}{+55x} & = & \color{red}{-55x} +10 \color{blue}{+55x} \color{blue}{-8} \\\Leftrightarrow & -132x+55x& = & 10-8 \\\Leftrightarrow & \color{red}{-77} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-77} & & \\\Leftrightarrow & x = \frac{-2}{77} & & \\ & V = \left\{ \frac{-2}{77} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+1)& = & 3x+\frac{8}{9} \\\Leftrightarrow & -35x-7& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 1 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-315}{ \color{blue}{9} }x- \frac{63}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -315x \color{red}{-63} & = & \color{red}{27x} +8 \\\Leftrightarrow & -315x \color{red}{-63} \color{blue}{+63} \color{blue}{-27x} & = & \color{red}{27x} +8 \color{blue}{-27x} \color{blue}{+63} \\\Leftrightarrow & -315x-27x& = & 8+63 \\\Leftrightarrow & \color{red}{-342} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-342} & & \\\Leftrightarrow & x = \frac{-71}{342} & & \\ & V = \left\{ \frac{-71}{342} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-28} & = & \color{red}{105x} +50 \\\Leftrightarrow & 280x \color{red}{-28} \color{blue}{+28} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{+28} \\\Leftrightarrow & 280x-105x& = & 50+28 \\\Leftrightarrow & \color{red}{175} x& = & 78 \\\Leftrightarrow & x = \frac{78}{175} & & \\ & V = \left\{ \frac{78}{175} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{3}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{12}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{12}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{35x} +8 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 84x-35x& = & 8+12 \\\Leftrightarrow & \color{red}{49} x& = & 20 \\\Leftrightarrow & x = \frac{20}{49} & & \\ & V = \left\{ \frac{20}{49} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{5}{11})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 18x+\frac{30}{11}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x+ \frac{150}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{+150} & = & \color{red}{-275x} +88 \\\Leftrightarrow & 990x \color{red}{+150} \color{blue}{-150} \color{blue}{+275x} & = & \color{red}{-275x} +88 \color{blue}{+275x} \color{blue}{-150} \\\Leftrightarrow & 990x+275x& = & 88-150 \\\Leftrightarrow & \color{red}{1265} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{1265} & & \\ & V = \left\{ \frac{-62}{1265} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -60x \color{red}{-12} & = & \color{red}{25x} +7 \\\Leftrightarrow & -60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +7 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & -60x-25x& = & 7+12 \\\Leftrightarrow & \color{red}{-85} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-85} & & \\\Leftrightarrow & x = \frac{-19}{85} & & \\ & V = \left\{ \frac{-19}{85} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{2}{11})& = & 3x+\frac{3}{8} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x- \frac{80}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{-80} & = & \color{red}{264x} +33 \\\Leftrightarrow & 880x \color{red}{-80} \color{blue}{+80} \color{blue}{-264x} & = & \color{red}{264x} +33 \color{blue}{-264x} \color{blue}{+80} \\\Leftrightarrow & 880x-264x& = & 33+80 \\\Leftrightarrow & \color{red}{616} x& = & 113 \\\Leftrightarrow & x = \frac{113}{616} & & \\ & V = \left\{ \frac{113}{616} \right\} & \\\end{align}\)