Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{5}{2})& = & 7x+\frac{10}{11} \\\Leftrightarrow & 15x+\frac{15}{2}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{330}{ \color{blue}{22} }x+ \frac{165}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 330x \color{red}{+165} & = & \color{red}{154x} +20 \\\Leftrightarrow & 330x \color{red}{+165} \color{blue}{-165} \color{blue}{-154x} & = & \color{red}{154x} +20 \color{blue}{-154x} \color{blue}{-165} \\\Leftrightarrow & 330x-154x& = & 20-165 \\\Leftrightarrow & \color{red}{176} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{176} & & \\ & V = \left\{ \frac{-145}{176} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{2}{3})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -21x+\frac{14}{3}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-189}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -189x \color{red}{+42} & = & \color{red}{72x} +4 \\\Leftrightarrow & -189x \color{red}{+42} \color{blue}{-42} \color{blue}{-72x} & = & \color{red}{72x} +4 \color{blue}{-72x} \color{blue}{-42} \\\Leftrightarrow & -189x-72x& = & 4-42 \\\Leftrightarrow & \color{red}{-261} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{-261} & & \\\Leftrightarrow & x = \frac{38}{261} & & \\ & V = \left\{ \frac{38}{261} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{7}{8} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1008}{ \color{blue}{56} }x- \frac{240}{ \color{blue}{56} })& = & (\frac{280}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1008x \color{red}{-240} & = & \color{red}{280x} +49 \\\Leftrightarrow & 1008x \color{red}{-240} \color{blue}{+240} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{+240} \\\Leftrightarrow & 1008x-280x& = & 49+240 \\\Leftrightarrow & \color{red}{728} x& = & 289 \\\Leftrightarrow & x = \frac{289}{728} & & \\ & V = \left\{ \frac{289}{728} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & 4x+\frac{8}{7} \\\Leftrightarrow & -35x-\frac{21}{8}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1960}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{224}{ \color{blue}{56} }x+ \frac{64}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1960x \color{red}{-147} & = & \color{red}{224x} +64 \\\Leftrightarrow & -1960x \color{red}{-147} \color{blue}{+147} \color{blue}{-224x} & = & \color{red}{224x} +64 \color{blue}{-224x} \color{blue}{+147} \\\Leftrightarrow & -1960x-224x& = & 64+147 \\\Leftrightarrow & \color{red}{-2184} x& = & 211 \\\Leftrightarrow & x = \frac{211}{-2184} & & \\\Leftrightarrow & x = \frac{-211}{2184} & & \\ & V = \left\{ \frac{-211}{2184} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{4}{7})& = & 7x+\frac{5}{3} \\\Leftrightarrow & -20x-\frac{16}{7}& = & 7x+\frac{5}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{35}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-48} & = & \color{red}{147x} +35 \\\Leftrightarrow & -420x \color{red}{-48} \color{blue}{+48} \color{blue}{-147x} & = & \color{red}{147x} +35 \color{blue}{-147x} \color{blue}{+48} \\\Leftrightarrow & -420x-147x& = & 35+48 \\\Leftrightarrow & \color{red}{-567} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-567} & & \\\Leftrightarrow & x = \frac{-83}{567} & & \\ & V = \left\{ \frac{-83}{567} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{3})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 4x-\frac{4}{3}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{28}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-28} & = & \color{red}{105x} +27 \\\Leftrightarrow & 84x \color{red}{-28} \color{blue}{+28} \color{blue}{-105x} & = & \color{red}{105x} +27 \color{blue}{-105x} \color{blue}{+28} \\\Leftrightarrow & 84x-105x& = & 27+28 \\\Leftrightarrow & \color{red}{-21} x& = & 55 \\\Leftrightarrow & x = \frac{55}{-21} & & \\\Leftrightarrow & x = \frac{-55}{21} & & \\ & V = \left\{ \frac{-55}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{2}{3})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{8}{3}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+40} & = & \color{red}{105x} +18 \\\Leftrightarrow & -300x \color{red}{+40} \color{blue}{-40} \color{blue}{-105x} & = & \color{red}{105x} +18 \color{blue}{-105x} \color{blue}{-40} \\\Leftrightarrow & -300x-105x& = & 18-40 \\\Leftrightarrow & \color{red}{-405} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-405} & & \\\Leftrightarrow & x = \frac{22}{405} & & \\ & V = \left\{ \frac{22}{405} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -30x-\frac{18}{5}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{-162} & = & \color{red}{315x} +25 \\\Leftrightarrow & -1350x \color{red}{-162} \color{blue}{+162} \color{blue}{-315x} & = & \color{red}{315x} +25 \color{blue}{-315x} \color{blue}{+162} \\\Leftrightarrow & -1350x-315x& = & 25+162 \\\Leftrightarrow & \color{red}{-1665} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-1665} & & \\\Leftrightarrow & x = \frac{-187}{1665} & & \\ & V = \left\{ \frac{-187}{1665} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{16}{3}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{-45}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{-80} & = & \color{red}{-45x} +18 \\\Leftrightarrow & 300x \color{red}{-80} \color{blue}{+80} \color{blue}{+45x} & = & \color{red}{-45x} +18 \color{blue}{+45x} \color{blue}{+80} \\\Leftrightarrow & 300x+45x& = & 18+80 \\\Leftrightarrow & \color{red}{345} x& = & 98 \\\Leftrightarrow & x = \frac{98}{345} & & \\ & V = \left\{ \frac{98}{345} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & -5x+\frac{5}{4} \\\Leftrightarrow & 4x-\frac{8}{3}& = & -5x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{48}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 48x \color{red}{-32} & = & \color{red}{-60x} +15 \\\Leftrightarrow & 48x \color{red}{-32} \color{blue}{+32} \color{blue}{+60x} & = & \color{red}{-60x} +15 \color{blue}{+60x} \color{blue}{+32} \\\Leftrightarrow & 48x+60x& = & 15+32 \\\Leftrightarrow & \color{red}{108} x& = & 47 \\\Leftrightarrow & x = \frac{47}{108} & & \\ & V = \left\{ \frac{47}{108} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x+\frac{3}{5})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 24x+\frac{18}{5}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x+ \frac{198}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{+198} & = & \color{red}{-275x} +50 \\\Leftrightarrow & 1320x \color{red}{+198} \color{blue}{-198} \color{blue}{+275x} & = & \color{red}{-275x} +50 \color{blue}{+275x} \color{blue}{-198} \\\Leftrightarrow & 1320x+275x& = & 50-198 \\\Leftrightarrow & \color{red}{1595} x& = & -148 \\\Leftrightarrow & x = \frac{-148}{1595} & & \\ & V = \left\{ \frac{-148}{1595} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-132} & = & \color{red}{-275x} +30 \\\Leftrightarrow & 660x \color{red}{-132} \color{blue}{+132} \color{blue}{+275x} & = & \color{red}{-275x} +30 \color{blue}{+275x} \color{blue}{+132} \\\Leftrightarrow & 660x+275x& = & 30+132 \\\Leftrightarrow & \color{red}{935} x& = & 162 \\\Leftrightarrow & x = \frac{162}{935} & & \\ & V = \left\{ \frac{162}{935} \right\} & \\\end{align}\)