Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{2}{11})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -6x-\frac{6}{11}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{30}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-30} & = & \color{red}{-385x} +88 \\\Leftrightarrow & -330x \color{red}{-30} \color{blue}{+30} \color{blue}{+385x} & = & \color{red}{-385x} +88 \color{blue}{+385x} \color{blue}{+30} \\\Leftrightarrow & -330x+385x& = & 88+30 \\\Leftrightarrow & \color{red}{55} x& = & 118 \\\Leftrightarrow & x = \frac{118}{55} & & \\ & V = \left\{ \frac{118}{55} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{3}{11})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -20x-\frac{15}{11}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2200}{ \color{blue}{110} }x- \frac{150}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2200x \color{red}{-150} & = & \color{red}{770x} +33 \\\Leftrightarrow & -2200x \color{red}{-150} \color{blue}{+150} \color{blue}{-770x} & = & \color{red}{770x} +33 \color{blue}{-770x} \color{blue}{+150} \\\Leftrightarrow & -2200x-770x& = & 33+150 \\\Leftrightarrow & \color{red}{-2970} x& = & 183 \\\Leftrightarrow & x = \frac{183}{-2970} & & \\\Leftrightarrow & x = \frac{-61}{990} & & \\ & V = \left\{ \frac{-61}{990} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x+\frac{3}{5})& = & 6x+\frac{5}{6} \\\Leftrightarrow & -18x+\frac{18}{5}& = & 6x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-540}{ \color{blue}{30} }x+ \frac{108}{ \color{blue}{30} })& = & (\frac{180}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -540x \color{red}{+108} & = & \color{red}{180x} +25 \\\Leftrightarrow & -540x \color{red}{+108} \color{blue}{-108} \color{blue}{-180x} & = & \color{red}{180x} +25 \color{blue}{-180x} \color{blue}{-108} \\\Leftrightarrow & -540x-180x& = & 25-108 \\\Leftrightarrow & \color{red}{-720} x& = & -83 \\\Leftrightarrow & x = \frac{-83}{-720} & & \\\Leftrightarrow & x = \frac{83}{720} & & \\ & V = \left\{ \frac{83}{720} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -3x+\frac{4}{11} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+66} & = & \color{red}{-231x} +28 \\\Leftrightarrow & 308x \color{red}{+66} \color{blue}{-66} \color{blue}{+231x} & = & \color{red}{-231x} +28 \color{blue}{+231x} \color{blue}{-66} \\\Leftrightarrow & 308x+231x& = & 28-66 \\\Leftrightarrow & \color{red}{539} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{539} & & \\ & V = \left\{ \frac{-38}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{2}{5})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-360}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -360x \color{red}{-48} & = & \color{red}{180x} +15 \\\Leftrightarrow & -360x \color{red}{-48} \color{blue}{+48} \color{blue}{-180x} & = & \color{red}{180x} +15 \color{blue}{-180x} \color{blue}{+48} \\\Leftrightarrow & -360x-180x& = & 15+48 \\\Leftrightarrow & \color{red}{-540} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-540} & & \\\Leftrightarrow & x = \frac{-7}{60} & & \\ & V = \left\{ \frac{-7}{60} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -9x+\frac{7}{6} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{-378}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{+60} & = & \color{red}{-378x} +49 \\\Leftrightarrow & -336x \color{red}{+60} \color{blue}{-60} \color{blue}{+378x} & = & \color{red}{-378x} +49 \color{blue}{+378x} \color{blue}{-60} \\\Leftrightarrow & -336x+378x& = & 49-60 \\\Leftrightarrow & \color{red}{42} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{42} & & \\ & V = \left\{ \frac{-11}{42} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{4}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & -9x-\frac{12}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{-50x} +3 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{+24} \\\Leftrightarrow & -90x+50x& = & 3+24 \\\Leftrightarrow & \color{red}{-40} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-40} & & \\\Leftrightarrow & x = \frac{-27}{40} & & \\ & V = \left\{ \frac{-27}{40} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{5}{8})& = & 4x+\frac{10}{9} \\\Leftrightarrow & -15x+\frac{25}{8}& = & 4x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1080}{ \color{blue}{72} }x+ \frac{225}{ \color{blue}{72} })& = & (\frac{288}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1080x \color{red}{+225} & = & \color{red}{288x} +80 \\\Leftrightarrow & -1080x \color{red}{+225} \color{blue}{-225} \color{blue}{-288x} & = & \color{red}{288x} +80 \color{blue}{-288x} \color{blue}{-225} \\\Leftrightarrow & -1080x-288x& = & 80-225 \\\Leftrightarrow & \color{red}{-1368} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-1368} & & \\\Leftrightarrow & x = \frac{145}{1368} & & \\ & V = \left\{ \frac{145}{1368} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{2}{9})& = & -5x+\frac{5}{7} \\\Leftrightarrow & -4x+\frac{4}{9}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{45}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+28} & = & \color{red}{-315x} +45 \\\Leftrightarrow & -252x \color{red}{+28} \color{blue}{-28} \color{blue}{+315x} & = & \color{red}{-315x} +45 \color{blue}{+315x} \color{blue}{-28} \\\Leftrightarrow & -252x+315x& = & 45-28 \\\Leftrightarrow & \color{red}{63} x& = & 17 \\\Leftrightarrow & x = \frac{17}{63} & & \\ & V = \left\{ \frac{17}{63} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{11})& = & -7x+\frac{5}{2} \\\Leftrightarrow & -30x+\frac{30}{11}& = & -7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x+ \frac{60}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{+60} & = & \color{red}{-154x} +55 \\\Leftrightarrow & -660x \color{red}{+60} \color{blue}{-60} \color{blue}{+154x} & = & \color{red}{-154x} +55 \color{blue}{+154x} \color{blue}{-60} \\\Leftrightarrow & -660x+154x& = & 55-60 \\\Leftrightarrow & \color{red}{-506} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-506} & & \\\Leftrightarrow & x = \frac{5}{506} & & \\ & V = \left\{ \frac{5}{506} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{12})& = & -6x+\frac{10}{11} \\\Leftrightarrow & -25x-\frac{25}{12}& = & -6x+\frac{10}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3300}{ \color{blue}{132} }x- \frac{275}{ \color{blue}{132} })& = & (\frac{-792}{ \color{blue}{132} }x+ \frac{120}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3300x \color{red}{-275} & = & \color{red}{-792x} +120 \\\Leftrightarrow & -3300x \color{red}{-275} \color{blue}{+275} \color{blue}{+792x} & = & \color{red}{-792x} +120 \color{blue}{+792x} \color{blue}{+275} \\\Leftrightarrow & -3300x+792x& = & 120+275 \\\Leftrightarrow & \color{red}{-2508} x& = & 395 \\\Leftrightarrow & x = \frac{395}{-2508} & & \\\Leftrightarrow & x = \frac{-395}{2508} & & \\ & V = \left\{ \frac{-395}{2508} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & 6x+\frac{2}{11} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 6x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{462}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-330} & = & \color{red}{462x} +14 \\\Leftrightarrow & -1386x \color{red}{-330} \color{blue}{+330} \color{blue}{-462x} & = & \color{red}{462x} +14 \color{blue}{-462x} \color{blue}{+330} \\\Leftrightarrow & -1386x-462x& = & 14+330 \\\Leftrightarrow & \color{red}{-1848} x& = & 344 \\\Leftrightarrow & x = \frac{344}{-1848} & & \\\Leftrightarrow & x = \frac{-43}{231} & & \\ & V = \left\{ \frac{-43}{231} \right\} & \\\end{align}\)