Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{4}{5} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{-12} & = & \color{red}{25x} +4 \\\Leftrightarrow & 60x \color{red}{-12} \color{blue}{+12} \color{blue}{-25x} & = & \color{red}{25x} +4 \color{blue}{-25x} \color{blue}{+12} \\\Leftrightarrow & 60x-25x& = & 4+12 \\\Leftrightarrow & \color{red}{35} x& = & 16 \\\Leftrightarrow & x = \frac{16}{35} & & \\ & V = \left\{ \frac{16}{35} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{6})& = & -3x+\frac{9}{2} \\\Leftrightarrow & 14x-\frac{35}{6}& = & -3x+\frac{9}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x- \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{-35} & = & \color{red}{-18x} +27 \\\Leftrightarrow & 84x \color{red}{-35} \color{blue}{+35} \color{blue}{+18x} & = & \color{red}{-18x} +27 \color{blue}{+18x} \color{blue}{+35} \\\Leftrightarrow & 84x+18x& = & 27+35 \\\Leftrightarrow & \color{red}{102} x& = & 62 \\\Leftrightarrow & x = \frac{62}{102} & & \\\Leftrightarrow & x = \frac{31}{51} & & \\ & V = \left\{ \frac{31}{51} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{3}{5})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{6}{5}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{+42} & = & \color{red}{245x} +50 \\\Leftrightarrow & -350x \color{red}{+42} \color{blue}{-42} \color{blue}{-245x} & = & \color{red}{245x} +50 \color{blue}{-245x} \color{blue}{-42} \\\Leftrightarrow & -350x-245x& = & 50-42 \\\Leftrightarrow & \color{red}{-595} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-595} & & \\\Leftrightarrow & x = \frac{-8}{595} & & \\ & V = \left\{ \frac{-8}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+10} & = & \color{red}{77x} +6 \\\Leftrightarrow & -110x \color{red}{+10} \color{blue}{-10} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-10} \\\Leftrightarrow & -110x-77x& = & 6-10 \\\Leftrightarrow & \color{red}{-187} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-187} & & \\\Leftrightarrow & x = \frac{4}{187} & & \\ & V = \left\{ \frac{4}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-176} & = & \color{red}{539x} +42 \\\Leftrightarrow & -1540x \color{red}{-176} \color{blue}{+176} \color{blue}{-539x} & = & \color{red}{539x} +42 \color{blue}{-539x} \color{blue}{+176} \\\Leftrightarrow & -1540x-539x& = & 42+176 \\\Leftrightarrow & \color{red}{-2079} x& = & 218 \\\Leftrightarrow & x = \frac{218}{-2079} & & \\\Leftrightarrow & x = \frac{-218}{2079} & & \\ & V = \left\{ \frac{-218}{2079} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{11})& = & -7x+\frac{7}{5} \\\Leftrightarrow & 15x-\frac{10}{11}& = & -7x+\frac{7}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{825}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{77}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 825x \color{red}{-50} & = & \color{red}{-385x} +77 \\\Leftrightarrow & 825x \color{red}{-50} \color{blue}{+50} \color{blue}{+385x} & = & \color{red}{-385x} +77 \color{blue}{+385x} \color{blue}{+50} \\\Leftrightarrow & 825x+385x& = & 77+50 \\\Leftrightarrow & \color{red}{1210} x& = & 127 \\\Leftrightarrow & x = \frac{127}{1210} & & \\ & V = \left\{ \frac{127}{1210} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{4}{5})& = & -9x+\frac{3}{10} \\\Leftrightarrow & -18x+\frac{24}{5}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-180}{ \color{blue}{10} }x+ \frac{48}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -180x \color{red}{+48} & = & \color{red}{-90x} +3 \\\Leftrightarrow & -180x \color{red}{+48} \color{blue}{-48} \color{blue}{+90x} & = & \color{red}{-90x} +3 \color{blue}{+90x} \color{blue}{-48} \\\Leftrightarrow & -180x+90x& = & 3-48 \\\Leftrightarrow & \color{red}{-90} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-90} & & \\\Leftrightarrow & x = \frac{1}{2} & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{4}{5})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x-\frac{12}{5}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-132} & = & \color{red}{385x} +30 \\\Leftrightarrow & -330x \color{red}{-132} \color{blue}{+132} \color{blue}{-385x} & = & \color{red}{385x} +30 \color{blue}{-385x} \color{blue}{+132} \\\Leftrightarrow & -330x-385x& = & 30+132 \\\Leftrightarrow & \color{red}{-715} x& = & 162 \\\Leftrightarrow & x = \frac{162}{-715} & & \\\Leftrightarrow & x = \frac{-162}{715} & & \\ & V = \left\{ \frac{-162}{715} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{4}{5})& = & -7x+\frac{2}{9} \\\Leftrightarrow & 24x+\frac{24}{5}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1080}{ \color{blue}{45} }x+ \frac{216}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1080x \color{red}{+216} & = & \color{red}{-315x} +10 \\\Leftrightarrow & 1080x \color{red}{+216} \color{blue}{-216} \color{blue}{+315x} & = & \color{red}{-315x} +10 \color{blue}{+315x} \color{blue}{-216} \\\Leftrightarrow & 1080x+315x& = & 10-216 \\\Leftrightarrow & \color{red}{1395} x& = & -206 \\\Leftrightarrow & x = \frac{-206}{1395} & & \\ & V = \left\{ \frac{-206}{1395} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{5})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 18x+\frac{24}{5}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{90}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 90x \color{red}{+24} & = & \color{red}{25x} +3 \\\Leftrightarrow & 90x \color{red}{+24} \color{blue}{-24} \color{blue}{-25x} & = & \color{red}{25x} +3 \color{blue}{-25x} \color{blue}{-24} \\\Leftrightarrow & 90x-25x& = & 3-24 \\\Leftrightarrow & \color{red}{65} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{65} & & \\ & V = \left\{ \frac{-21}{65} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{9})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{8}{9}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{-8} & = & \color{red}{-63x} +30 \\\Leftrightarrow & -90x \color{red}{-8} \color{blue}{+8} \color{blue}{+63x} & = & \color{red}{-63x} +30 \color{blue}{+63x} \color{blue}{+8} \\\Leftrightarrow & -90x+63x& = & 30+8 \\\Leftrightarrow & \color{red}{-27} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-27} & & \\\Leftrightarrow & x = \frac{-38}{27} & & \\ & V = \left\{ \frac{-38}{27} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{3})& = & -2x+\frac{9}{7} \\\Leftrightarrow & 21x+\frac{35}{3}& = & -2x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{-42}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+245} & = & \color{red}{-42x} +27 \\\Leftrightarrow & 441x \color{red}{+245} \color{blue}{-245} \color{blue}{+42x} & = & \color{red}{-42x} +27 \color{blue}{+42x} \color{blue}{-245} \\\Leftrightarrow & 441x+42x& = & 27-245 \\\Leftrightarrow & \color{red}{483} x& = & -218 \\\Leftrightarrow & x = \frac{-218}{483} & & \\ & V = \left\{ \frac{-218}{483} \right\} & \\\end{align}\)