Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{4})& = & 2x+\frac{3}{11} \\\Leftrightarrow & 35x-\frac{35}{4}& = & 2x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1540}{ \color{blue}{44} }x- \frac{385}{ \color{blue}{44} })& = & (\frac{88}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1540x \color{red}{-385} & = & \color{red}{88x} +12 \\\Leftrightarrow & 1540x \color{red}{-385} \color{blue}{+385} \color{blue}{-88x} & = & \color{red}{88x} +12 \color{blue}{-88x} \color{blue}{+385} \\\Leftrightarrow & 1540x-88x& = & 12+385 \\\Leftrightarrow & \color{red}{1452} x& = & 397 \\\Leftrightarrow & x = \frac{397}{1452} & & \\ & V = \left\{ \frac{397}{1452} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{2}{9})& = & -2x+\frac{9}{7} \\\Leftrightarrow & -28x-\frac{14}{9}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1764}{ \color{blue}{63} }x- \frac{98}{ \color{blue}{63} })& = & (\frac{-126}{ \color{blue}{63} }x+ \frac{81}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1764x \color{red}{-98} & = & \color{red}{-126x} +81 \\\Leftrightarrow & -1764x \color{red}{-98} \color{blue}{+98} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{+98} \\\Leftrightarrow & -1764x+126x& = & 81+98 \\\Leftrightarrow & \color{red}{-1638} x& = & 179 \\\Leftrightarrow & x = \frac{179}{-1638} & & \\\Leftrightarrow & x = \frac{-179}{1638} & & \\ & V = \left\{ \frac{-179}{1638} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{2}{7})& = & 5x+\frac{2}{9} \\\Leftrightarrow & -9x-\frac{6}{7}& = & 5x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-567}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -567x \color{red}{-54} & = & \color{red}{315x} +14 \\\Leftrightarrow & -567x \color{red}{-54} \color{blue}{+54} \color{blue}{-315x} & = & \color{red}{315x} +14 \color{blue}{-315x} \color{blue}{+54} \\\Leftrightarrow & -567x-315x& = & 14+54 \\\Leftrightarrow & \color{red}{-882} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-882} & & \\\Leftrightarrow & x = \frac{-34}{441} & & \\ & V = \left\{ \frac{-34}{441} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{7})& = & -5x+\frac{10}{11} \\\Leftrightarrow & -12x-\frac{20}{7}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-220} & = & \color{red}{-385x} +70 \\\Leftrightarrow & -924x \color{red}{-220} \color{blue}{+220} \color{blue}{+385x} & = & \color{red}{-385x} +70 \color{blue}{+385x} \color{blue}{+220} \\\Leftrightarrow & -924x+385x& = & 70+220 \\\Leftrightarrow & \color{red}{-539} x& = & 290 \\\Leftrightarrow & x = \frac{290}{-539} & & \\\Leftrightarrow & x = \frac{-290}{539} & & \\ & V = \left\{ \frac{-290}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{2})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{25}{2}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{30}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{-4}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 30x \color{red}{-25} & = & \color{red}{-4x} +9 \\\Leftrightarrow & 30x \color{red}{-25} \color{blue}{+25} \color{blue}{+4x} & = & \color{red}{-4x} +9 \color{blue}{+4x} \color{blue}{+25} \\\Leftrightarrow & 30x+4x& = & 9+25 \\\Leftrightarrow & \color{red}{34} x& = & 34 \\\Leftrightarrow & x = \frac{34}{34} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{5}{3})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -35x+\frac{35}{3}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-1155}{ \color{blue}{33} }x+ \frac{385}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -1155x \color{red}{+385} & = & \color{red}{-99x} +18 \\\Leftrightarrow & -1155x \color{red}{+385} \color{blue}{-385} \color{blue}{+99x} & = & \color{red}{-99x} +18 \color{blue}{+99x} \color{blue}{-385} \\\Leftrightarrow & -1155x+99x& = & 18-385 \\\Leftrightarrow & \color{red}{-1056} x& = & -367 \\\Leftrightarrow & x = \frac{-367}{-1056} & & \\\Leftrightarrow & x = \frac{367}{1056} & & \\ & V = \left\{ \frac{367}{1056} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{5}{4})& = & 5x+\frac{8}{3} \\\Leftrightarrow & -9x-\frac{15}{4}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-108}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -108x \color{red}{-45} & = & \color{red}{60x} +32 \\\Leftrightarrow & -108x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +32 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & -108x-60x& = & 32+45 \\\Leftrightarrow & \color{red}{-168} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-168} & & \\\Leftrightarrow & x = \frac{-11}{24} & & \\ & V = \left\{ \frac{-11}{24} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{4}{3})& = & 9x+\frac{8}{9} \\\Leftrightarrow & -20x-\frac{16}{3}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{48}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-48} & = & \color{red}{81x} +8 \\\Leftrightarrow & -180x \color{red}{-48} \color{blue}{+48} \color{blue}{-81x} & = & \color{red}{81x} +8 \color{blue}{-81x} \color{blue}{+48} \\\Leftrightarrow & -180x-81x& = & 8+48 \\\Leftrightarrow & \color{red}{-261} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-261} & & \\\Leftrightarrow & x = \frac{-56}{261} & & \\ & V = \left\{ \frac{-56}{261} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{2}{11})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{14}{11}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{42}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-42} & = & \color{red}{297x} +22 \\\Leftrightarrow & 462x \color{red}{-42} \color{blue}{+42} \color{blue}{-297x} & = & \color{red}{297x} +22 \color{blue}{-297x} \color{blue}{+42} \\\Leftrightarrow & 462x-297x& = & 22+42 \\\Leftrightarrow & \color{red}{165} x& = & 64 \\\Leftrightarrow & x = \frac{64}{165} & & \\ & V = \left\{ \frac{64}{165} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{1}{2})& = & -3x+\frac{5}{11} \\\Leftrightarrow & -28x-\frac{7}{2}& = & -3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-616}{ \color{blue}{22} }x- \frac{77}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -616x \color{red}{-77} & = & \color{red}{-66x} +10 \\\Leftrightarrow & -616x \color{red}{-77} \color{blue}{+77} \color{blue}{+66x} & = & \color{red}{-66x} +10 \color{blue}{+66x} \color{blue}{+77} \\\Leftrightarrow & -616x+66x& = & 10+77 \\\Leftrightarrow & \color{red}{-550} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-550} & & \\\Leftrightarrow & x = \frac{-87}{550} & & \\ & V = \left\{ \frac{-87}{550} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{6})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -21x+\frac{35}{6}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{+35} & = & \color{red}{48x} +20 \\\Leftrightarrow & -126x \color{red}{+35} \color{blue}{-35} \color{blue}{-48x} & = & \color{red}{48x} +20 \color{blue}{-48x} \color{blue}{-35} \\\Leftrightarrow & -126x-48x& = & 20-35 \\\Leftrightarrow & \color{red}{-174} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-174} & & \\\Leftrightarrow & x = \frac{5}{58} & & \\ & V = \left\{ \frac{5}{58} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{7})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{20}{7}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+220} & = & \color{red}{693x} +42 \\\Leftrightarrow & -616x \color{red}{+220} \color{blue}{-220} \color{blue}{-693x} & = & \color{red}{693x} +42 \color{blue}{-693x} \color{blue}{-220} \\\Leftrightarrow & -616x-693x& = & 42-220 \\\Leftrightarrow & \color{red}{-1309} x& = & -178 \\\Leftrightarrow & x = \frac{-178}{-1309} & & \\\Leftrightarrow & x = \frac{178}{1309} & & \\ & V = \left\{ \frac{178}{1309} \right\} & \\\end{align}\)