Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-56}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -56x \color{red}{+12} & = & \color{red}{70x} +49 \\\Leftrightarrow & -56x \color{red}{+12} \color{blue}{-12} \color{blue}{-70x} & = & \color{red}{70x} +49 \color{blue}{-70x} \color{blue}{-12} \\\Leftrightarrow & -56x-70x& = & 49-12 \\\Leftrightarrow & \color{red}{-126} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-126} & & \\\Leftrightarrow & x = \frac{-37}{126} & & \\ & V = \left\{ \frac{-37}{126} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{7})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{700}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} })& = & (\frac{-84}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 700x \color{red}{+40} & = & \color{red}{-84x} +63 \\\Leftrightarrow & 700x \color{red}{+40} \color{blue}{-40} \color{blue}{+84x} & = & \color{red}{-84x} +63 \color{blue}{+84x} \color{blue}{-40} \\\Leftrightarrow & 700x+84x& = & 63-40 \\\Leftrightarrow & \color{red}{784} x& = & 23 \\\Leftrightarrow & x = \frac{23}{784} & & \\ & V = \left\{ \frac{23}{784} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{4}{9})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -6x+\frac{8}{9}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} })& = & (\frac{252}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+32} & = & \color{red}{252x} +63 \\\Leftrightarrow & -216x \color{red}{+32} \color{blue}{-32} \color{blue}{-252x} & = & \color{red}{252x} +63 \color{blue}{-252x} \color{blue}{-32} \\\Leftrightarrow & -216x-252x& = & 63-32 \\\Leftrightarrow & \color{red}{-468} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-468} & & \\\Leftrightarrow & x = \frac{-31}{468} & & \\ & V = \left\{ \frac{-31}{468} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{5}{3})& = & 3x+\frac{4}{11} \\\Leftrightarrow & 20x-\frac{20}{3}& = & 3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-220} & = & \color{red}{99x} +12 \\\Leftrightarrow & 660x \color{red}{-220} \color{blue}{+220} \color{blue}{-99x} & = & \color{red}{99x} +12 \color{blue}{-99x} \color{blue}{+220} \\\Leftrightarrow & 660x-99x& = & 12+220 \\\Leftrightarrow & \color{red}{561} x& = & 232 \\\Leftrightarrow & x = \frac{232}{561} & & \\ & V = \left\{ \frac{232}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{2})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 10x-\frac{25}{2}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{20}{ \color{blue}{2} }x- \frac{25}{ \color{blue}{2} })& = & (\frac{-14}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & 20x \color{red}{-25} & = & \color{red}{-14x} +9 \\\Leftrightarrow & 20x \color{red}{-25} \color{blue}{+25} \color{blue}{+14x} & = & \color{red}{-14x} +9 \color{blue}{+14x} \color{blue}{+25} \\\Leftrightarrow & 20x+14x& = & 9+25 \\\Leftrightarrow & \color{red}{34} x& = & 34 \\\Leftrightarrow & x = \frac{34}{34} & & \\\Leftrightarrow & x = 1 & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{4}{7})& = & -9x+\frac{7}{10} \\\Leftrightarrow & -8x+\frac{16}{7}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x+ \frac{160}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{+160} & = & \color{red}{-630x} +49 \\\Leftrightarrow & -560x \color{red}{+160} \color{blue}{-160} \color{blue}{+630x} & = & \color{red}{-630x} +49 \color{blue}{+630x} \color{blue}{-160} \\\Leftrightarrow & -560x+630x& = & 49-160 \\\Leftrightarrow & \color{red}{70} x& = & -111 \\\Leftrightarrow & x = \frac{-111}{70} & & \\ & V = \left\{ \frac{-111}{70} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{2}{7})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{6}{7}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{315}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 315x \color{red}{-18} & = & \color{red}{84x} +28 \\\Leftrightarrow & 315x \color{red}{-18} \color{blue}{+18} \color{blue}{-84x} & = & \color{red}{84x} +28 \color{blue}{-84x} \color{blue}{+18} \\\Leftrightarrow & 315x-84x& = & 28+18 \\\Leftrightarrow & \color{red}{231} x& = & 46 \\\Leftrightarrow & x = \frac{46}{231} & & \\ & V = \left\{ \frac{46}{231} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & 5x+\frac{8}{7} \\\Leftrightarrow & -24x-\frac{24}{7}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-168}{ \color{blue}{7} }x- \frac{24}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -168x \color{red}{-24} & = & \color{red}{35x} +8 \\\Leftrightarrow & -168x \color{red}{-24} \color{blue}{+24} \color{blue}{-35x} & = & \color{red}{35x} +8 \color{blue}{-35x} \color{blue}{+24} \\\Leftrightarrow & -168x-35x& = & 8+24 \\\Leftrightarrow & \color{red}{-203} x& = & 32 \\\Leftrightarrow & x = \frac{32}{-203} & & \\\Leftrightarrow & x = \frac{-32}{203} & & \\ & V = \left\{ \frac{-32}{203} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{3}{7})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{-105x} +14 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +14 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 126x+105x& = & 14+18 \\\Leftrightarrow & \color{red}{231} x& = & 32 \\\Leftrightarrow & x = \frac{32}{231} & & \\ & V = \left\{ \frac{32}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{5}{11})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 8x-\frac{20}{11}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x- \frac{180}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{-180} & = & \color{red}{693x} +44 \\\Leftrightarrow & 792x \color{red}{-180} \color{blue}{+180} \color{blue}{-693x} & = & \color{red}{693x} +44 \color{blue}{-693x} \color{blue}{+180} \\\Leftrightarrow & 792x-693x& = & 44+180 \\\Leftrightarrow & \color{red}{99} x& = & 224 \\\Leftrightarrow & x = \frac{224}{99} & & \\ & V = \left\{ \frac{224}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{10}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{189x} +30 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +30 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & -168x-189x& = & 30-140 \\\Leftrightarrow & \color{red}{-357} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{-357} & & \\\Leftrightarrow & x = \frac{110}{357} & & \\ & V = \left\{ \frac{110}{357} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{9})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -12x-\frac{20}{9}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-216}{ \color{blue}{18} }x- \frac{40}{ \color{blue}{18} })& = & (\frac{90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -216x \color{red}{-40} & = & \color{red}{90x} +81 \\\Leftrightarrow & -216x \color{red}{-40} \color{blue}{+40} \color{blue}{-90x} & = & \color{red}{90x} +81 \color{blue}{-90x} \color{blue}{+40} \\\Leftrightarrow & -216x-90x& = & 81+40 \\\Leftrightarrow & \color{red}{-306} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-306} & & \\\Leftrightarrow & x = \frac{-121}{306} & & \\ & V = \left\{ \frac{-121}{306} \right\} & \\\end{align}\)