Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{+70} & = & \color{red}{120x} +6 \\\Leftrightarrow & -315x \color{red}{+70} \color{blue}{-70} \color{blue}{-120x} & = & \color{red}{120x} +6 \color{blue}{-120x} \color{blue}{-70} \\\Leftrightarrow & -315x-120x& = & 6-70 \\\Leftrightarrow & \color{red}{-435} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-435} & & \\\Leftrightarrow & x = \frac{64}{435} & & \\ & V = \left\{ \frac{64}{435} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{11})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -24x-\frac{30}{11}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1056}{ \color{blue}{44} }x- \frac{120}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1056x \color{red}{-120} & = & \color{red}{-220x} +77 \\\Leftrightarrow & -1056x \color{red}{-120} \color{blue}{+120} \color{blue}{+220x} & = & \color{red}{-220x} +77 \color{blue}{+220x} \color{blue}{+120} \\\Leftrightarrow & -1056x+220x& = & 77+120 \\\Leftrightarrow & \color{red}{-836} x& = & 197 \\\Leftrightarrow & x = \frac{197}{-836} & & \\\Leftrightarrow & x = \frac{-197}{836} & & \\ & V = \left\{ \frac{-197}{836} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{9})& = & 9x+\frac{5}{3} \\\Leftrightarrow & -8x-\frac{20}{9}& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{20}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{15}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-20} & = & \color{red}{81x} +15 \\\Leftrightarrow & -72x \color{red}{-20} \color{blue}{+20} \color{blue}{-81x} & = & \color{red}{81x} +15 \color{blue}{-81x} \color{blue}{+20} \\\Leftrightarrow & -72x-81x& = & 15+20 \\\Leftrightarrow & \color{red}{-153} x& = & 35 \\\Leftrightarrow & x = \frac{35}{-153} & & \\\Leftrightarrow & x = \frac{-35}{153} & & \\ & V = \left\{ \frac{-35}{153} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x+\frac{4}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-450}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -450x \color{red}{+20} & = & \color{red}{-315x} +54 \\\Leftrightarrow & -450x \color{red}{+20} \color{blue}{-20} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{-20} \\\Leftrightarrow & -450x+315x& = & 54-20 \\\Leftrightarrow & \color{red}{-135} x& = & 34 \\\Leftrightarrow & x = \frac{34}{-135} & & \\\Leftrightarrow & x = \frac{-34}{135} & & \\ & V = \left\{ \frac{-34}{135} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{4}{3})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 25x-\frac{20}{3}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{75}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 75x \color{red}{-20} & = & \color{red}{27x} +10 \\\Leftrightarrow & 75x \color{red}{-20} \color{blue}{+20} \color{blue}{-27x} & = & \color{red}{27x} +10 \color{blue}{-27x} \color{blue}{+20} \\\Leftrightarrow & 75x-27x& = & 10+20 \\\Leftrightarrow & \color{red}{48} x& = & 30 \\\Leftrightarrow & x = \frac{30}{48} & & \\\Leftrightarrow & x = \frac{5}{8} & & \\ & V = \left\{ \frac{5}{8} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & -12x-\frac{30}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{-150} & = & \color{red}{175x} +49 \\\Leftrightarrow & -420x \color{red}{-150} \color{blue}{+150} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{+150} \\\Leftrightarrow & -420x-175x& = & 49+150 \\\Leftrightarrow & \color{red}{-595} x& = & 199 \\\Leftrightarrow & x = \frac{199}{-595} & & \\\Leftrightarrow & x = \frac{-199}{595} & & \\ & V = \left\{ \frac{-199}{595} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{2}{7})& = & -8x+\frac{4}{11} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -8x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1155}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-616}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1155x \color{red}{-110} & = & \color{red}{-616x} +28 \\\Leftrightarrow & 1155x \color{red}{-110} \color{blue}{+110} \color{blue}{+616x} & = & \color{red}{-616x} +28 \color{blue}{+616x} \color{blue}{+110} \\\Leftrightarrow & 1155x+616x& = & 28+110 \\\Leftrightarrow & \color{red}{1771} x& = & 138 \\\Leftrightarrow & x = \frac{138}{1771} & & \\\Leftrightarrow & x = \frac{6}{77} & & \\ & V = \left\{ \frac{6}{77} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{3}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & -9x+\frac{9}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-126}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -126x \color{red}{+18} & = & \color{red}{-70x} +63 \\\Leftrightarrow & -126x \color{red}{+18} \color{blue}{-18} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{-18} \\\Leftrightarrow & -126x+70x& = & 63-18 \\\Leftrightarrow & \color{red}{-56} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-56} & & \\\Leftrightarrow & x = \frac{-45}{56} & & \\ & V = \left\{ \frac{-45}{56} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{7}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{-25x} +7 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +7 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & 90x+25x& = & 7-24 \\\Leftrightarrow & \color{red}{115} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{115} & & \\ & V = \left\{ \frac{-17}{115} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{3}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 50-36 \\\Leftrightarrow & \color{red}{255} x& = & 14 \\\Leftrightarrow & x = \frac{14}{255} & & \\ & V = \left\{ \frac{14}{255} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -7x+\frac{7}{12} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{300}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{-84x} +7 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{+84x} & = & \color{red}{-84x} +7 \color{blue}{+84x} \color{blue}{-80} \\\Leftrightarrow & 300x+84x& = & 7-80 \\\Leftrightarrow & \color{red}{384} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{384} & & \\ & V = \left\{ \frac{-73}{384} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{2}{7})& = & 2x+\frac{5}{11} \\\Leftrightarrow & 9x-\frac{6}{7}& = & 2x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-66} & = & \color{red}{154x} +35 \\\Leftrightarrow & 693x \color{red}{-66} \color{blue}{+66} \color{blue}{-154x} & = & \color{red}{154x} +35 \color{blue}{-154x} \color{blue}{+66} \\\Leftrightarrow & 693x-154x& = & 35+66 \\\Leftrightarrow & \color{red}{539} x& = & 101 \\\Leftrightarrow & x = \frac{101}{539} & & \\ & V = \left\{ \frac{101}{539} \right\} & \\\end{align}\)