Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{5}{4})& = & 5x+\frac{2}{11} \\\Leftrightarrow & 28x+\frac{35}{4}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1232}{ \color{blue}{44} }x+ \frac{385}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{8}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1232x \color{red}{+385} & = & \color{red}{220x} +8 \\\Leftrightarrow & 1232x \color{red}{+385} \color{blue}{-385} \color{blue}{-220x} & = & \color{red}{220x} +8 \color{blue}{-220x} \color{blue}{-385} \\\Leftrightarrow & 1232x-220x& = & 8-385 \\\Leftrightarrow & \color{red}{1012} x& = & -377 \\\Leftrightarrow & x = \frac{-377}{1012} & & \\ & V = \left\{ \frac{-377}{1012} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x-\frac{5}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -20x+\frac{20}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-300}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -300x \color{red}{+100} & = & \color{red}{-105x} +18 \\\Leftrightarrow & -300x \color{red}{+100} \color{blue}{-100} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-100} \\\Leftrightarrow & -300x+105x& = & 18-100 \\\Leftrightarrow & \color{red}{-195} x& = & -82 \\\Leftrightarrow & x = \frac{-82}{-195} & & \\\Leftrightarrow & x = \frac{82}{195} & & \\ & V = \left\{ \frac{82}{195} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{-225x} +36 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{+225x} & = & \color{red}{-225x} +36 \color{blue}{+225x} \color{blue}{-20} \\\Leftrightarrow & -180x+225x& = & 36-20 \\\Leftrightarrow & \color{red}{45} x& = & 16 \\\Leftrightarrow & x = \frac{16}{45} & & \\ & V = \left\{ \frac{16}{45} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & -3x+\frac{7}{9} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -3x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{+30} & = & \color{red}{-27x} +7 \\\Leftrightarrow & 90x \color{red}{+30} \color{blue}{-30} \color{blue}{+27x} & = & \color{red}{-27x} +7 \color{blue}{+27x} \color{blue}{-30} \\\Leftrightarrow & 90x+27x& = & 7-30 \\\Leftrightarrow & \color{red}{117} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{117} & & \\ & V = \left\{ \frac{-23}{117} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{5})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{480}{ \color{blue}{40} }x- \frac{96}{ \color{blue}{40} })& = & (\frac{200}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 480x \color{red}{-96} & = & \color{red}{200x} +15 \\\Leftrightarrow & 480x \color{red}{-96} \color{blue}{+96} \color{blue}{-200x} & = & \color{red}{200x} +15 \color{blue}{-200x} \color{blue}{+96} \\\Leftrightarrow & 480x-200x& = & 15+96 \\\Leftrightarrow & \color{red}{280} x& = & 111 \\\Leftrightarrow & x = \frac{111}{280} & & \\ & V = \left\{ \frac{111}{280} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{4}{9})& = & -3x+\frac{7}{3} \\\Leftrightarrow & -8x-\frac{8}{9}& = & -3x+\frac{7}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{21}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{-8} & = & \color{red}{-27x} +21 \\\Leftrightarrow & -72x \color{red}{-8} \color{blue}{+8} \color{blue}{+27x} & = & \color{red}{-27x} +21 \color{blue}{+27x} \color{blue}{+8} \\\Leftrightarrow & -72x+27x& = & 21+8 \\\Leftrightarrow & \color{red}{-45} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-45} & & \\\Leftrightarrow & x = \frac{-29}{45} & & \\ & V = \left\{ \frac{-29}{45} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+20} & = & \color{red}{9x} +4 \\\Leftrightarrow & 48x \color{red}{+20} \color{blue}{-20} \color{blue}{-9x} & = & \color{red}{9x} +4 \color{blue}{-9x} \color{blue}{-20} \\\Leftrightarrow & 48x-9x& = & 4-20 \\\Leftrightarrow & \color{red}{39} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{39} & & \\ & V = \left\{ \frac{-16}{39} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{10})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 12x-\frac{9}{10}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{99}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-99} & = & \color{red}{550x} +80 \\\Leftrightarrow & 1320x \color{red}{-99} \color{blue}{+99} \color{blue}{-550x} & = & \color{red}{550x} +80 \color{blue}{-550x} \color{blue}{+99} \\\Leftrightarrow & 1320x-550x& = & 80+99 \\\Leftrightarrow & \color{red}{770} x& = & 179 \\\Leftrightarrow & x = \frac{179}{770} & & \\ & V = \left\{ \frac{179}{770} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{3}{5})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 20x-\frac{12}{5}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-108} & = & \color{red}{135x} +20 \\\Leftrightarrow & 900x \color{red}{-108} \color{blue}{+108} \color{blue}{-135x} & = & \color{red}{135x} +20 \color{blue}{-135x} \color{blue}{+108} \\\Leftrightarrow & 900x-135x& = & 20+108 \\\Leftrightarrow & \color{red}{765} x& = & 128 \\\Leftrightarrow & x = \frac{128}{765} & & \\ & V = \left\{ \frac{128}{765} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{11})& = & 5x+\frac{9}{10} \\\Leftrightarrow & 12x-\frac{12}{11}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{1320}{ \color{blue}{110} }x- \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 1320x \color{red}{-120} & = & \color{red}{550x} +99 \\\Leftrightarrow & 1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-550x} & = & \color{red}{550x} +99 \color{blue}{-550x} \color{blue}{+120} \\\Leftrightarrow & 1320x-550x& = & 99+120 \\\Leftrightarrow & \color{red}{770} x& = & 219 \\\Leftrightarrow & x = \frac{219}{770} & & \\ & V = \left\{ \frac{219}{770} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{2}{9})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{8}{9}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-540}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -540x \color{red}{+40} & = & \color{red}{225x} +54 \\\Leftrightarrow & -540x \color{red}{+40} \color{blue}{-40} \color{blue}{-225x} & = & \color{red}{225x} +54 \color{blue}{-225x} \color{blue}{-40} \\\Leftrightarrow & -540x-225x& = & 54-40 \\\Leftrightarrow & \color{red}{-765} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-765} & & \\\Leftrightarrow & x = \frac{-14}{765} & & \\ & V = \left\{ \frac{-14}{765} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{3}{8})& = & 9x+\frac{5}{2} \\\Leftrightarrow & 28x-\frac{21}{8}& = & 9x+\frac{5}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{20}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 224x \color{red}{-21} & = & \color{red}{72x} +20 \\\Leftrightarrow & 224x \color{red}{-21} \color{blue}{+21} \color{blue}{-72x} & = & \color{red}{72x} +20 \color{blue}{-72x} \color{blue}{+21} \\\Leftrightarrow & 224x-72x& = & 20+21 \\\Leftrightarrow & \color{red}{152} x& = & 41 \\\Leftrightarrow & x = \frac{41}{152} & & \\ & V = \left\{ \frac{41}{152} \right\} & \\\end{align}\)