Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 126x+105x& = & 14+18 \\\Leftrightarrow & \color{red}{231} x& = & 32 \\\Leftrightarrow & x = \frac{32}{231} & & \\ & V = \left\{ \frac{32}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{2}{3})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -20x+\frac{8}{3}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -60x \color{red}{+8} & = & \color{red}{-9x} +4 \\\Leftrightarrow & -60x \color{red}{+8} \color{blue}{-8} \color{blue}{+9x} & = & \color{red}{-9x} +4 \color{blue}{+9x} \color{blue}{-8} \\\Leftrightarrow & -60x+9x& = & 4-8 \\\Leftrightarrow & \color{red}{-51} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-51} & & \\\Leftrightarrow & x = \frac{4}{51} & & \\ & V = \left\{ \frac{4}{51} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{5}{3})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 20x+\frac{20}{3}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{240}{ \color{blue}{12} }x+ \frac{80}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 240x \color{red}{+80} & = & \color{red}{-36x} +27 \\\Leftrightarrow & 240x \color{red}{+80} \color{blue}{-80} \color{blue}{+36x} & = & \color{red}{-36x} +27 \color{blue}{+36x} \color{blue}{-80} \\\Leftrightarrow & 240x+36x& = & 27-80 \\\Leftrightarrow & \color{red}{276} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{276} & & \\ & V = \left\{ \frac{-53}{276} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{2}{9})& = & -5x+\frac{9}{10} \\\Leftrightarrow & 6x-\frac{4}{9}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{40}{ \color{blue}{90} })& = & (\frac{-450}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-40} & = & \color{red}{-450x} +81 \\\Leftrightarrow & 540x \color{red}{-40} \color{blue}{+40} \color{blue}{+450x} & = & \color{red}{-450x} +81 \color{blue}{+450x} \color{blue}{+40} \\\Leftrightarrow & 540x+450x& = & 81+40 \\\Leftrightarrow & \color{red}{990} x& = & 121 \\\Leftrightarrow & x = \frac{121}{990} & & \\\Leftrightarrow & x = \frac{11}{90} & & \\ & V = \left\{ \frac{11}{90} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{4}{9})& = & 9x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{20}{9}& = & 9x+\frac{3}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-1800}{ \color{blue}{90} }x- \frac{200}{ \color{blue}{90} })& = & (\frac{810}{ \color{blue}{90} }x+ \frac{27}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -1800x \color{red}{-200} & = & \color{red}{810x} +27 \\\Leftrightarrow & -1800x \color{red}{-200} \color{blue}{+200} \color{blue}{-810x} & = & \color{red}{810x} +27 \color{blue}{-810x} \color{blue}{+200} \\\Leftrightarrow & -1800x-810x& = & 27+200 \\\Leftrightarrow & \color{red}{-2610} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-2610} & & \\\Leftrightarrow & x = \frac{-227}{2610} & & \\ & V = \left\{ \frac{-227}{2610} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{11})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 25x-\frac{10}{11}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2475}{ \color{blue}{99} }x- \frac{90}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{77}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2475x \color{red}{-90} & = & \color{red}{693x} +77 \\\Leftrightarrow & 2475x \color{red}{-90} \color{blue}{+90} \color{blue}{-693x} & = & \color{red}{693x} +77 \color{blue}{-693x} \color{blue}{+90} \\\Leftrightarrow & 2475x-693x& = & 77+90 \\\Leftrightarrow & \color{red}{1782} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1782} & & \\ & V = \left\{ \frac{167}{1782} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{3}{8})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 35x-\frac{21}{8}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{448}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{-147} & = & \color{red}{448x} +48 \\\Leftrightarrow & 1960x \color{red}{-147} \color{blue}{+147} \color{blue}{-448x} & = & \color{red}{448x} +48 \color{blue}{-448x} \color{blue}{+147} \\\Leftrightarrow & 1960x-448x& = & 48+147 \\\Leftrightarrow & \color{red}{1512} x& = & 195 \\\Leftrightarrow & x = \frac{195}{1512} & & \\\Leftrightarrow & x = \frac{65}{504} & & \\ & V = \left\{ \frac{65}{504} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{4}{3})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 4x+\frac{8}{3}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 24x \color{red}{+16} & = & \color{red}{-42x} +9 \\\Leftrightarrow & 24x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & 24x+42x& = & 9-16 \\\Leftrightarrow & \color{red}{66} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{66} & & \\ & V = \left\{ \frac{-7}{66} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{11})& = & 5x+\frac{5}{7} \\\Leftrightarrow & -12x+\frac{6}{11}& = & 5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+42} & = & \color{red}{385x} +55 \\\Leftrightarrow & -924x \color{red}{+42} \color{blue}{-42} \color{blue}{-385x} & = & \color{red}{385x} +55 \color{blue}{-385x} \color{blue}{-42} \\\Leftrightarrow & -924x-385x& = & 55-42 \\\Leftrightarrow & \color{red}{-1309} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-1309} & & \\\Leftrightarrow & x = \frac{-13}{1309} & & \\ & V = \left\{ \frac{-13}{1309} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & -24x-\frac{18}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-504}{ \color{blue}{21} }x- \frac{54}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -504x \color{red}{-54} & = & \color{red}{-105x} +14 \\\Leftrightarrow & -504x \color{red}{-54} \color{blue}{+54} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+54} \\\Leftrightarrow & -504x+105x& = & 14+54 \\\Leftrightarrow & \color{red}{-399} x& = & 68 \\\Leftrightarrow & x = \frac{68}{-399} & & \\\Leftrightarrow & x = \frac{-68}{399} & & \\ & V = \left\{ \frac{-68}{399} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -16x+\frac{8}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-112}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -112x \color{red}{+8} & = & \color{red}{49x} +10 \\\Leftrightarrow & -112x \color{red}{+8} \color{blue}{-8} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-8} \\\Leftrightarrow & -112x-49x& = & 10-8 \\\Leftrightarrow & \color{red}{-161} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-161} & & \\\Leftrightarrow & x = \frac{-2}{161} & & \\ & V = \left\{ \frac{-2}{161} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{7})& = & -3x+\frac{10}{9} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-90} & = & \color{red}{-189x} +70 \\\Leftrightarrow & 630x \color{red}{-90} \color{blue}{+90} \color{blue}{+189x} & = & \color{red}{-189x} +70 \color{blue}{+189x} \color{blue}{+90} \\\Leftrightarrow & 630x+189x& = & 70+90 \\\Leftrightarrow & \color{red}{819} x& = & 160 \\\Leftrightarrow & x = \frac{160}{819} & & \\ & V = \left\{ \frac{160}{819} \right\} & \\\end{align}\)