Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{3}{11})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -18x+\frac{18}{11}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1782}{ \color{blue}{99} }x+ \frac{162}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{110}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1782x \color{red}{+162} & = & \color{red}{693x} +110 \\\Leftrightarrow & -1782x \color{red}{+162} \color{blue}{-162} \color{blue}{-693x} & = & \color{red}{693x} +110 \color{blue}{-693x} \color{blue}{-162} \\\Leftrightarrow & -1782x-693x& = & 110-162 \\\Leftrightarrow & \color{red}{-2475} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-2475} & & \\\Leftrightarrow & x = \frac{52}{2475} & & \\ & V = \left\{ \frac{52}{2475} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x-\frac{2}{3})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -14x+\frac{14}{3}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x+ \frac{70}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{+70} & = & \color{red}{45x} +6 \\\Leftrightarrow & -210x \color{red}{+70} \color{blue}{-70} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-70} \\\Leftrightarrow & -210x-45x& = & 6-70 \\\Leftrightarrow & \color{red}{-255} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{-255} & & \\\Leftrightarrow & x = \frac{64}{255} & & \\ & V = \left\{ \frac{64}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & 7x+\frac{2}{9} \\\Leftrightarrow & 8x+\frac{6}{7}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{504}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{14}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 504x \color{red}{+54} & = & \color{red}{441x} +14 \\\Leftrightarrow & 504x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +14 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 504x-441x& = & 14-54 \\\Leftrightarrow & \color{red}{63} x& = & -40 \\\Leftrightarrow & x = \frac{-40}{63} & & \\ & V = \left\{ \frac{-40}{63} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{10})& = & 8x+\frac{9}{10} \\\Leftrightarrow & 15x+\frac{9}{10}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+9} & = & \color{red}{80x} +9 \\\Leftrightarrow & 150x \color{red}{+9} \color{blue}{-9} \color{blue}{-80x} & = & \color{red}{80x} +9 \color{blue}{-80x} \color{blue}{-9} \\\Leftrightarrow & 150x-80x& = & 9-9 \\\Leftrightarrow & \color{red}{70} x& = & 0 \\\Leftrightarrow & x = \frac{0}{70} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & 7x+\frac{6}{5} \\\Leftrightarrow & -16x-\frac{12}{11}& = & 7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-880}{ \color{blue}{55} }x- \frac{60}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -880x \color{red}{-60} & = & \color{red}{385x} +66 \\\Leftrightarrow & -880x \color{red}{-60} \color{blue}{+60} \color{blue}{-385x} & = & \color{red}{385x} +66 \color{blue}{-385x} \color{blue}{+60} \\\Leftrightarrow & -880x-385x& = & 66+60 \\\Leftrightarrow & \color{red}{-1265} x& = & 126 \\\Leftrightarrow & x = \frac{126}{-1265} & & \\\Leftrightarrow & x = \frac{-126}{1265} & & \\ & V = \left\{ \frac{-126}{1265} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{9})& = & 3x+\frac{2}{9} \\\Leftrightarrow & 20x+\frac{20}{9}& = & 3x+\frac{2}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{2}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+20} & = & \color{red}{27x} +2 \\\Leftrightarrow & 180x \color{red}{+20} \color{blue}{-20} \color{blue}{-27x} & = & \color{red}{27x} +2 \color{blue}{-27x} \color{blue}{-20} \\\Leftrightarrow & 180x-27x& = & 2-20 \\\Leftrightarrow & \color{red}{153} x& = & -18 \\\Leftrightarrow & x = \frac{-18}{153} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & 9x+\frac{2}{3} \\\Leftrightarrow & 14x+\frac{35}{6}& = & 9x+\frac{2}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{54}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+35} & = & \color{red}{54x} +4 \\\Leftrightarrow & 84x \color{red}{+35} \color{blue}{-35} \color{blue}{-54x} & = & \color{red}{54x} +4 \color{blue}{-54x} \color{blue}{-35} \\\Leftrightarrow & 84x-54x& = & 4-35 \\\Leftrightarrow & \color{red}{30} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{30} & & \\ & V = \left\{ \frac{-31}{30} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+80} & = & \color{red}{-75x} +27 \\\Leftrightarrow & -180x \color{red}{+80} \color{blue}{-80} \color{blue}{+75x} & = & \color{red}{-75x} +27 \color{blue}{+75x} \color{blue}{-80} \\\Leftrightarrow & -180x+75x& = & 27-80 \\\Leftrightarrow & \color{red}{-105} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-105} & & \\\Leftrightarrow & x = \frac{53}{105} & & \\ & V = \left\{ \frac{53}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{11})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{8}{11}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{88}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{33}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 88x \color{red}{-8} & = & \color{red}{33x} +5 \\\Leftrightarrow & 88x \color{red}{-8} \color{blue}{+8} \color{blue}{-33x} & = & \color{red}{33x} +5 \color{blue}{-33x} \color{blue}{+8} \\\Leftrightarrow & 88x-33x& = & 5+8 \\\Leftrightarrow & \color{red}{55} x& = & 13 \\\Leftrightarrow & x = \frac{13}{55} & & \\ & V = \left\{ \frac{13}{55} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{3}{2})& = & -4x+\frac{5}{6} \\\Leftrightarrow & 15x-\frac{15}{2}& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{45}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-45} & = & \color{red}{-24x} +5 \\\Leftrightarrow & 90x \color{red}{-45} \color{blue}{+45} \color{blue}{+24x} & = & \color{red}{-24x} +5 \color{blue}{+24x} \color{blue}{+45} \\\Leftrightarrow & 90x+24x& = & 5+45 \\\Leftrightarrow & \color{red}{114} x& = & 50 \\\Leftrightarrow & x = \frac{50}{114} & & \\\Leftrightarrow & x = \frac{25}{57} & & \\ & V = \left\{ \frac{25}{57} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{4}{9})& = & 8x+\frac{7}{4} \\\Leftrightarrow & -15x-\frac{20}{9}& = & 8x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-540}{ \color{blue}{36} }x- \frac{80}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -540x \color{red}{-80} & = & \color{red}{288x} +63 \\\Leftrightarrow & -540x \color{red}{-80} \color{blue}{+80} \color{blue}{-288x} & = & \color{red}{288x} +63 \color{blue}{-288x} \color{blue}{+80} \\\Leftrightarrow & -540x-288x& = & 63+80 \\\Leftrightarrow & \color{red}{-828} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-828} & & \\\Leftrightarrow & x = \frac{-143}{828} & & \\ & V = \left\{ \frac{-143}{828} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -30x-\frac{12}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-450}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -450x \color{red}{-36} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -450x \color{red}{-36} \color{blue}{+36} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{+36} \\\Leftrightarrow & -450x+105x& = & 20+36 \\\Leftrightarrow & \color{red}{-345} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-345} & & \\\Leftrightarrow & x = \frac{-56}{345} & & \\ & V = \left\{ \frac{-56}{345} \right\} & \\\end{align}\)