Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{2})& = & -7x+\frac{3}{10} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -7x+\frac{3}{10} \\ & & & \text{kgv van noemers 2 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{250}{ \color{blue}{10} }x+ \frac{125}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 250x \color{red}{+125} & = & \color{red}{-70x} +3 \\\Leftrightarrow & 250x \color{red}{+125} \color{blue}{-125} \color{blue}{+70x} & = & \color{red}{-70x} +3 \color{blue}{+70x} \color{blue}{-125} \\\Leftrightarrow & 250x+70x& = & 3-125 \\\Leftrightarrow & \color{red}{320} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{320} & & \\\Leftrightarrow & x = \frac{-61}{160} & & \\ & V = \left\{ \frac{-61}{160} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{4}{11})& = & -7x+\frac{5}{12} \\\Leftrightarrow & 24x-\frac{24}{11}& = & -7x+\frac{5}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{3168}{ \color{blue}{132} }x- \frac{288}{ \color{blue}{132} })& = & (\frac{-924}{ \color{blue}{132} }x+ \frac{55}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & 3168x \color{red}{-288} & = & \color{red}{-924x} +55 \\\Leftrightarrow & 3168x \color{red}{-288} \color{blue}{+288} \color{blue}{+924x} & = & \color{red}{-924x} +55 \color{blue}{+924x} \color{blue}{+288} \\\Leftrightarrow & 3168x+924x& = & 55+288 \\\Leftrightarrow & \color{red}{4092} x& = & 343 \\\Leftrightarrow & x = \frac{343}{4092} & & \\ & V = \left\{ \frac{343}{4092} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{5}{7})& = & -7x+\frac{3}{11} \\\Leftrightarrow & -16x-\frac{20}{7}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1232}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1232x \color{red}{-220} & = & \color{red}{-539x} +21 \\\Leftrightarrow & -1232x \color{red}{-220} \color{blue}{+220} \color{blue}{+539x} & = & \color{red}{-539x} +21 \color{blue}{+539x} \color{blue}{+220} \\\Leftrightarrow & -1232x+539x& = & 21+220 \\\Leftrightarrow & \color{red}{-693} x& = & 241 \\\Leftrightarrow & x = \frac{241}{-693} & & \\\Leftrightarrow & x = \frac{-241}{693} & & \\ & V = \left\{ \frac{-241}{693} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{3})& = & -7x+\frac{7}{9} \\\Leftrightarrow & -16x+\frac{8}{3}& = & -7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+24} & = & \color{red}{-63x} +7 \\\Leftrightarrow & -144x \color{red}{+24} \color{blue}{-24} \color{blue}{+63x} & = & \color{red}{-63x} +7 \color{blue}{+63x} \color{blue}{-24} \\\Leftrightarrow & -144x+63x& = & 7-24 \\\Leftrightarrow & \color{red}{-81} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-81} & & \\\Leftrightarrow & x = \frac{17}{81} & & \\ & V = \left\{ \frac{17}{81} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{9})& = & 5x+\frac{4}{5} \\\Leftrightarrow & -4x+\frac{10}{9}& = & 5x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-180}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} })& = & (\frac{225}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -180x \color{red}{+50} & = & \color{red}{225x} +36 \\\Leftrightarrow & -180x \color{red}{+50} \color{blue}{-50} \color{blue}{-225x} & = & \color{red}{225x} +36 \color{blue}{-225x} \color{blue}{-50} \\\Leftrightarrow & -180x-225x& = & 36-50 \\\Leftrightarrow & \color{red}{-405} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-405} & & \\\Leftrightarrow & x = \frac{14}{405} & & \\ & V = \left\{ \frac{14}{405} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{252}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 252x \color{red}{+90} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 252x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & 252x+147x& = & 14-90 \\\Leftrightarrow & \color{red}{399} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{399} & & \\\Leftrightarrow & x = \frac{-4}{21} & & \\ & V = \left\{ \frac{-4}{21} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{3}{5})& = & -5x+\frac{3}{10} \\\Leftrightarrow & 12x+\frac{9}{5}& = & -5x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{18}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+18} & = & \color{red}{-50x} +3 \\\Leftrightarrow & 120x \color{red}{+18} \color{blue}{-18} \color{blue}{+50x} & = & \color{red}{-50x} +3 \color{blue}{+50x} \color{blue}{-18} \\\Leftrightarrow & 120x+50x& = & 3-18 \\\Leftrightarrow & \color{red}{170} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{170} & & \\\Leftrightarrow & x = \frac{-3}{34} & & \\ & V = \left\{ \frac{-3}{34} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{2}{5})& = & -5x+\frac{4}{7} \\\Leftrightarrow & -24x-\frac{12}{5}& = & -5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{-84} & = & \color{red}{-175x} +20 \\\Leftrightarrow & -840x \color{red}{-84} \color{blue}{+84} \color{blue}{+175x} & = & \color{red}{-175x} +20 \color{blue}{+175x} \color{blue}{+84} \\\Leftrightarrow & -840x+175x& = & 20+84 \\\Leftrightarrow & \color{red}{-665} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-665} & & \\\Leftrightarrow & x = \frac{-104}{665} & & \\ & V = \left\{ \frac{-104}{665} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{5}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{-18} & = & \color{red}{25x} +6 \\\Leftrightarrow & -120x \color{red}{-18} \color{blue}{+18} \color{blue}{-25x} & = & \color{red}{25x} +6 \color{blue}{-25x} \color{blue}{+18} \\\Leftrightarrow & -120x-25x& = & 6+18 \\\Leftrightarrow & \color{red}{-145} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-145} & & \\\Leftrightarrow & x = \frac{-24}{145} & & \\ & V = \left\{ \frac{-24}{145} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{11})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 15x-\frac{15}{11}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{990}{ \color{blue}{66} }x- \frac{90}{ \color{blue}{66} })& = & (\frac{132}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{132x} +55 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{-132x} & = & \color{red}{132x} +55 \color{blue}{-132x} \color{blue}{+90} \\\Leftrightarrow & 990x-132x& = & 55+90 \\\Leftrightarrow & \color{red}{858} x& = & 145 \\\Leftrightarrow & x = \frac{145}{858} & & \\ & V = \left\{ \frac{145}{858} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{4}{5})& = & -8x+\frac{7}{2} \\\Leftrightarrow & 21x-\frac{28}{5}& = & -8x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x- \frac{56}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{-56} & = & \color{red}{-80x} +35 \\\Leftrightarrow & 210x \color{red}{-56} \color{blue}{+56} \color{blue}{+80x} & = & \color{red}{-80x} +35 \color{blue}{+80x} \color{blue}{+56} \\\Leftrightarrow & 210x+80x& = & 35+56 \\\Leftrightarrow & \color{red}{290} x& = & 91 \\\Leftrightarrow & x = \frac{91}{290} & & \\ & V = \left\{ \frac{91}{290} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 6x+\frac{12}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{+36} & = & \color{red}{105x} +14 \\\Leftrightarrow & 126x \color{red}{+36} \color{blue}{-36} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{-36} \\\Leftrightarrow & 126x-105x& = & 14-36 \\\Leftrightarrow & \color{red}{21} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{21} & & \\ & V = \left\{ \frac{-22}{21} \right\} & \\\end{align}\)