Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{6})& = & -7x+\frac{2}{9} \\\Leftrightarrow & -20x-\frac{25}{6}& = & -7x+\frac{2}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-360}{ \color{blue}{18} }x- \frac{75}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{4}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -360x \color{red}{-75} & = & \color{red}{-126x} +4 \\\Leftrightarrow & -360x \color{red}{-75} \color{blue}{+75} \color{blue}{+126x} & = & \color{red}{-126x} +4 \color{blue}{+126x} \color{blue}{+75} \\\Leftrightarrow & -360x+126x& = & 4+75 \\\Leftrightarrow & \color{red}{-234} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-234} & & \\\Leftrightarrow & x = \frac{-79}{234} & & \\ & V = \left\{ \frac{-79}{234} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 9x+\frac{3}{4} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 9x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-112}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{252}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -112x \color{red}{-24} & = & \color{red}{252x} +21 \\\Leftrightarrow & -112x \color{red}{-24} \color{blue}{+24} \color{blue}{-252x} & = & \color{red}{252x} +21 \color{blue}{-252x} \color{blue}{+24} \\\Leftrightarrow & -112x-252x& = & 21+24 \\\Leftrightarrow & \color{red}{-364} x& = & 45 \\\Leftrightarrow & x = \frac{45}{-364} & & \\\Leftrightarrow & x = \frac{-45}{364} & & \\ & V = \left\{ \frac{-45}{364} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{2}{7})& = & -5x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{6}{7}& = & -5x+\frac{6}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-6} & = & \color{red}{-35x} +6 \\\Leftrightarrow & 84x \color{red}{-6} \color{blue}{+6} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+6} \\\Leftrightarrow & 84x+35x& = & 6+6 \\\Leftrightarrow & \color{red}{119} x& = & 12 \\\Leftrightarrow & x = \frac{12}{119} & & \\ & V = \left\{ \frac{12}{119} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{4}{7})& = & 3x+\frac{9}{10} \\\Leftrightarrow & 20x+\frac{20}{7}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1400}{ \color{blue}{70} }x+ \frac{200}{ \color{blue}{70} })& = & (\frac{210}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1400x \color{red}{+200} & = & \color{red}{210x} +63 \\\Leftrightarrow & 1400x \color{red}{+200} \color{blue}{-200} \color{blue}{-210x} & = & \color{red}{210x} +63 \color{blue}{-210x} \color{blue}{-200} \\\Leftrightarrow & 1400x-210x& = & 63-200 \\\Leftrightarrow & \color{red}{1190} x& = & -137 \\\Leftrightarrow & x = \frac{-137}{1190} & & \\ & V = \left\{ \frac{-137}{1190} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{5}{7})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -4x-\frac{10}{7}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{-189}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{-30} & = & \color{red}{-189x} +28 \\\Leftrightarrow & -84x \color{red}{-30} \color{blue}{+30} \color{blue}{+189x} & = & \color{red}{-189x} +28 \color{blue}{+189x} \color{blue}{+30} \\\Leftrightarrow & -84x+189x& = & 28+30 \\\Leftrightarrow & \color{red}{105} x& = & 58 \\\Leftrightarrow & x = \frac{58}{105} & & \\ & V = \left\{ \frac{58}{105} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{2}{3})& = & -7x+\frac{5}{7} \\\Leftrightarrow & 8x-\frac{8}{3}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{-56} & = & \color{red}{-147x} +15 \\\Leftrightarrow & 168x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +15 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & 168x+147x& = & 15+56 \\\Leftrightarrow & \color{red}{315} x& = & 71 \\\Leftrightarrow & x = \frac{71}{315} & & \\ & V = \left\{ \frac{71}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{2}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{+36} \color{blue}{-36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{-36} \\\Leftrightarrow & -180x-75x& = & 50-36 \\\Leftrightarrow & \color{red}{-255} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-255} & & \\\Leftrightarrow & x = \frac{-14}{255} & & \\ & V = \left\{ \frac{-14}{255} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & -7x+\frac{7}{12} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{7}{12} \\ & & & \text{kgv van noemers 9 en 12 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-576}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{21}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -576x \color{red}{+32} & = & \color{red}{-252x} +21 \\\Leftrightarrow & -576x \color{red}{+32} \color{blue}{-32} \color{blue}{+252x} & = & \color{red}{-252x} +21 \color{blue}{+252x} \color{blue}{-32} \\\Leftrightarrow & -576x+252x& = & 21-32 \\\Leftrightarrow & \color{red}{-324} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-324} & & \\\Leftrightarrow & x = \frac{11}{324} & & \\ & V = \left\{ \frac{11}{324} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{3}{2})& = & 9x+\frac{2}{5} \\\Leftrightarrow & 14x-\frac{21}{2}& = & 9x+\frac{2}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{140}{ \color{blue}{10} }x- \frac{105}{ \color{blue}{10} })& = & (\frac{90}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 140x \color{red}{-105} & = & \color{red}{90x} +4 \\\Leftrightarrow & 140x \color{red}{-105} \color{blue}{+105} \color{blue}{-90x} & = & \color{red}{90x} +4 \color{blue}{-90x} \color{blue}{+105} \\\Leftrightarrow & 140x-90x& = & 4+105 \\\Leftrightarrow & \color{red}{50} x& = & 109 \\\Leftrightarrow & x = \frac{109}{50} & & \\ & V = \left\{ \frac{109}{50} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 14x-\frac{35}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{462}{ \color{blue}{33} }x- \frac{105}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 462x \color{red}{-105} & = & \color{red}{-297x} +44 \\\Leftrightarrow & 462x \color{red}{-105} \color{blue}{+105} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{+105} \\\Leftrightarrow & 462x+297x& = & 44+105 \\\Leftrightarrow & \color{red}{759} x& = & 149 \\\Leftrightarrow & x = \frac{149}{759} & & \\ & V = \left\{ \frac{149}{759} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{9})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 20x-\frac{8}{9}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{1800}{ \color{blue}{90} }x- \frac{80}{ \color{blue}{90} })& = & (\frac{-810}{ \color{blue}{90} }x+ \frac{63}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 1800x \color{red}{-80} & = & \color{red}{-810x} +63 \\\Leftrightarrow & 1800x \color{red}{-80} \color{blue}{+80} \color{blue}{+810x} & = & \color{red}{-810x} +63 \color{blue}{+810x} \color{blue}{+80} \\\Leftrightarrow & 1800x+810x& = & 63+80 \\\Leftrightarrow & \color{red}{2610} x& = & 143 \\\Leftrightarrow & x = \frac{143}{2610} & & \\ & V = \left\{ \frac{143}{2610} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{7})& = & 2x+\frac{3}{10} \\\Leftrightarrow & 15x+\frac{6}{7}& = & 2x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{1050}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{140}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 1050x \color{red}{+60} & = & \color{red}{140x} +21 \\\Leftrightarrow & 1050x \color{red}{+60} \color{blue}{-60} \color{blue}{-140x} & = & \color{red}{140x} +21 \color{blue}{-140x} \color{blue}{-60} \\\Leftrightarrow & 1050x-140x& = & 21-60 \\\Leftrightarrow & \color{red}{910} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{910} & & \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)