Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -9x-\frac{6}{11}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{-594}{ \color{blue}{66} }x- \frac{36}{ \color{blue}{66} })& = & (\frac{462}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & -594x \color{red}{-36} & = & \color{red}{462x} +55 \\\Leftrightarrow & -594x \color{red}{-36} \color{blue}{+36} \color{blue}{-462x} & = & \color{red}{462x} +55 \color{blue}{-462x} \color{blue}{+36} \\\Leftrightarrow & -594x-462x& = & 55+36 \\\Leftrightarrow & \color{red}{-1056} x& = & 91 \\\Leftrightarrow & x = \frac{91}{-1056} & & \\\Leftrightarrow & x = \frac{-91}{1056} & & \\ & V = \left\{ \frac{-91}{1056} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x- \frac{28}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{-28} & = & \color{red}{-175x} +50 \\\Leftrightarrow & 140x \color{red}{-28} \color{blue}{+28} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+28} \\\Leftrightarrow & 140x+175x& = & 50+28 \\\Leftrightarrow & \color{red}{315} x& = & 78 \\\Leftrightarrow & x = \frac{78}{315} & & \\\Leftrightarrow & x = \frac{26}{105} & & \\ & V = \left\{ \frac{26}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{2}{3})& = & -8x+\frac{2}{9} \\\Leftrightarrow & -21x-\frac{14}{3}& = & -8x+\frac{2}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x- \frac{42}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{-42} & = & \color{red}{-72x} +2 \\\Leftrightarrow & -189x \color{red}{-42} \color{blue}{+42} \color{blue}{+72x} & = & \color{red}{-72x} +2 \color{blue}{+72x} \color{blue}{+42} \\\Leftrightarrow & -189x+72x& = & 2+42 \\\Leftrightarrow & \color{red}{-117} x& = & 44 \\\Leftrightarrow & x = \frac{44}{-117} & & \\\Leftrightarrow & x = \frac{-44}{117} & & \\ & V = \left\{ \frac{-44}{117} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & 7x+\frac{5}{7} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+42} & = & \color{red}{539x} +55 \\\Leftrightarrow & -462x \color{red}{+42} \color{blue}{-42} \color{blue}{-539x} & = & \color{red}{539x} +55 \color{blue}{-539x} \color{blue}{-42} \\\Leftrightarrow & -462x-539x& = & 55-42 \\\Leftrightarrow & \color{red}{-1001} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-1001} & & \\\Leftrightarrow & x = \frac{-1}{77} & & \\ & V = \left\{ \frac{-1}{77} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{2}{5})& = & -5x+\frac{10}{7} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-84} & = & \color{red}{-175x} +50 \\\Leftrightarrow & -840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +50 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -840x+175x& = & 50+84 \\\Leftrightarrow & \color{red}{-665} x& = & 134 \\\Leftrightarrow & x = \frac{134}{-665} & & \\\Leftrightarrow & x = \frac{-134}{665} & & \\ & V = \left\{ \frac{-134}{665} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{1}{2})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -20x+\frac{5}{2}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x+ \frac{45}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{8}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{+45} & = & \color{red}{-126x} +8 \\\Leftrightarrow & -360x \color{red}{+45} \color{blue}{-45} \color{blue}{+126x} & = & \color{red}{-126x} +8 \color{blue}{+126x} \color{blue}{-45} \\\Leftrightarrow & -360x+126x& = & 8-45 \\\Leftrightarrow & \color{red}{-234} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-234} & & \\\Leftrightarrow & x = \frac{37}{234} & & \\ & V = \left\{ \frac{37}{234} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{2}{11})& = & -5x+\frac{2}{7} \\\Leftrightarrow & 6x+\frac{6}{11}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{462}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 462x \color{red}{+42} & = & \color{red}{-385x} +22 \\\Leftrightarrow & 462x \color{red}{+42} \color{blue}{-42} \color{blue}{+385x} & = & \color{red}{-385x} +22 \color{blue}{+385x} \color{blue}{-42} \\\Leftrightarrow & 462x+385x& = & 22-42 \\\Leftrightarrow & \color{red}{847} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{847} & & \\ & V = \left\{ \frac{-20}{847} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{5}{2})& = & -3x+\frac{2}{5} \\\Leftrightarrow & 20x+\frac{25}{2}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{200}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{-30}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 200x \color{red}{+125} & = & \color{red}{-30x} +4 \\\Leftrightarrow & 200x \color{red}{+125} \color{blue}{-125} \color{blue}{+30x} & = & \color{red}{-30x} +4 \color{blue}{+30x} \color{blue}{-125} \\\Leftrightarrow & 200x+30x& = & 4-125 \\\Leftrightarrow & \color{red}{230} x& = & -121 \\\Leftrightarrow & x = \frac{-121}{230} & & \\ & V = \left\{ \frac{-121}{230} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-132}{ \color{blue}{11} }x+ \frac{24}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -132x \color{red}{+24} & = & \color{red}{55x} +7 \\\Leftrightarrow & -132x \color{red}{+24} \color{blue}{-24} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{-24} \\\Leftrightarrow & -132x-55x& = & 7-24 \\\Leftrightarrow & \color{red}{-187} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-187} & & \\\Leftrightarrow & x = \frac{1}{11} & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{11})& = & 2x+\frac{7}{9} \\\Leftrightarrow & -28x+\frac{35}{11}& = & 2x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{+315} & = & \color{red}{198x} +77 \\\Leftrightarrow & -2772x \color{red}{+315} \color{blue}{-315} \color{blue}{-198x} & = & \color{red}{198x} +77 \color{blue}{-198x} \color{blue}{-315} \\\Leftrightarrow & -2772x-198x& = & 77-315 \\\Leftrightarrow & \color{red}{-2970} x& = & -238 \\\Leftrightarrow & x = \frac{-238}{-2970} & & \\\Leftrightarrow & x = \frac{119}{1485} & & \\ & V = \left\{ \frac{119}{1485} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-270}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -270x \color{red}{-108} & = & \color{red}{315x} +20 \\\Leftrightarrow & -270x \color{red}{-108} \color{blue}{+108} \color{blue}{-315x} & = & \color{red}{315x} +20 \color{blue}{-315x} \color{blue}{+108} \\\Leftrightarrow & -270x-315x& = & 20+108 \\\Leftrightarrow & \color{red}{-585} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-585} & & \\\Leftrightarrow & x = \frac{-128}{585} & & \\ & V = \left\{ \frac{-128}{585} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{4}{5})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x+\frac{28}{5}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{84}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+84} & = & \color{red}{-45x} +20 \\\Leftrightarrow & -210x \color{red}{+84} \color{blue}{-84} \color{blue}{+45x} & = & \color{red}{-45x} +20 \color{blue}{+45x} \color{blue}{-84} \\\Leftrightarrow & -210x+45x& = & 20-84 \\\Leftrightarrow & \color{red}{-165} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-165} & & \\\Leftrightarrow & x = \frac{64}{165} & & \\ & V = \left\{ \frac{64}{165} \right\} & \\\end{align}\)