Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & 3x+\frac{9}{7} \\\Leftrightarrow & -20x-\frac{12}{5}& = & 3x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-700}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -700x \color{red}{-84} & = & \color{red}{105x} +45 \\\Leftrightarrow & -700x \color{red}{-84} \color{blue}{+84} \color{blue}{-105x} & = & \color{red}{105x} +45 \color{blue}{-105x} \color{blue}{+84} \\\Leftrightarrow & -700x-105x& = & 45+84 \\\Leftrightarrow & \color{red}{-805} x& = & 129 \\\Leftrightarrow & x = \frac{129}{-805} & & \\\Leftrightarrow & x = \frac{-129}{805} & & \\ & V = \left\{ \frac{-129}{805} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -6x+\frac{15}{4}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-72}{ \color{blue}{12} }x+ \frac{45}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -72x \color{red}{+45} & = & \color{red}{84x} +32 \\\Leftrightarrow & -72x \color{red}{+45} \color{blue}{-45} \color{blue}{-84x} & = & \color{red}{84x} +32 \color{blue}{-84x} \color{blue}{-45} \\\Leftrightarrow & -72x-84x& = & 32-45 \\\Leftrightarrow & \color{red}{-156} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-156} & & \\\Leftrightarrow & x = \frac{1}{12} & & \\ & V = \left\{ \frac{1}{12} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{8})& = & 8x+\frac{4}{11} \\\Leftrightarrow & 15x+\frac{15}{8}& = & 8x+\frac{4}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1320}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{32}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1320x \color{red}{+165} & = & \color{red}{704x} +32 \\\Leftrightarrow & 1320x \color{red}{+165} \color{blue}{-165} \color{blue}{-704x} & = & \color{red}{704x} +32 \color{blue}{-704x} \color{blue}{-165} \\\Leftrightarrow & 1320x-704x& = & 32-165 \\\Leftrightarrow & \color{red}{616} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{616} & & \\\Leftrightarrow & x = \frac{-19}{88} & & \\ & V = \left\{ \frac{-19}{88} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{4}{9} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1584}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1584x \color{red}{-108} & = & \color{red}{-693x} +44 \\\Leftrightarrow & -1584x \color{red}{-108} \color{blue}{+108} \color{blue}{+693x} & = & \color{red}{-693x} +44 \color{blue}{+693x} \color{blue}{+108} \\\Leftrightarrow & -1584x+693x& = & 44+108 \\\Leftrightarrow & \color{red}{-891} x& = & 152 \\\Leftrightarrow & x = \frac{152}{-891} & & \\\Leftrightarrow & x = \frac{-152}{891} & & \\ & V = \left\{ \frac{-152}{891} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & 9x+\frac{3}{8} \\\Leftrightarrow & 8x+\frac{4}{5}& = & 9x+\frac{3}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{320}{ \color{blue}{40} }x+ \frac{32}{ \color{blue}{40} })& = & (\frac{360}{ \color{blue}{40} }x+ \frac{15}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 320x \color{red}{+32} & = & \color{red}{360x} +15 \\\Leftrightarrow & 320x \color{red}{+32} \color{blue}{-32} \color{blue}{-360x} & = & \color{red}{360x} +15 \color{blue}{-360x} \color{blue}{-32} \\\Leftrightarrow & 320x-360x& = & 15-32 \\\Leftrightarrow & \color{red}{-40} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-40} & & \\\Leftrightarrow & x = \frac{17}{40} & & \\ & V = \left\{ \frac{17}{40} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{1}{3})& = & 3x+\frac{7}{10} \\\Leftrightarrow & 14x+\frac{7}{3}& = & 3x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{420}{ \color{blue}{30} }x+ \frac{70}{ \color{blue}{30} })& = & (\frac{90}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 420x \color{red}{+70} & = & \color{red}{90x} +21 \\\Leftrightarrow & 420x \color{red}{+70} \color{blue}{-70} \color{blue}{-90x} & = & \color{red}{90x} +21 \color{blue}{-90x} \color{blue}{-70} \\\Leftrightarrow & 420x-90x& = & 21-70 \\\Leftrightarrow & \color{red}{330} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{330} & & \\ & V = \left\{ \frac{-49}{330} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{5}{7})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{25}{7}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{50}{ \color{blue}{14} })& = & (\frac{-126}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+50} & = & \color{red}{-126x} +63 \\\Leftrightarrow & -280x \color{red}{+50} \color{blue}{-50} \color{blue}{+126x} & = & \color{red}{-126x} +63 \color{blue}{+126x} \color{blue}{-50} \\\Leftrightarrow & -280x+126x& = & 63-50 \\\Leftrightarrow & \color{red}{-154} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-154} & & \\\Leftrightarrow & x = \frac{-13}{154} & & \\ & V = \left\{ \frac{-13}{154} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{9})& = & -3x+\frac{8}{11} \\\Leftrightarrow & -14x+\frac{28}{9}& = & -3x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1386}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1386x \color{red}{+308} & = & \color{red}{-297x} +72 \\\Leftrightarrow & -1386x \color{red}{+308} \color{blue}{-308} \color{blue}{+297x} & = & \color{red}{-297x} +72 \color{blue}{+297x} \color{blue}{-308} \\\Leftrightarrow & -1386x+297x& = & 72-308 \\\Leftrightarrow & \color{red}{-1089} x& = & -236 \\\Leftrightarrow & x = \frac{-236}{-1089} & & \\\Leftrightarrow & x = \frac{236}{1089} & & \\ & V = \left\{ \frac{236}{1089} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{4}{3})& = & 8x+\frac{5}{2} \\\Leftrightarrow & -21x-\frac{28}{3}& = & 8x+\frac{5}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-126}{ \color{blue}{6} }x- \frac{56}{ \color{blue}{6} })& = & (\frac{48}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -126x \color{red}{-56} & = & \color{red}{48x} +15 \\\Leftrightarrow & -126x \color{red}{-56} \color{blue}{+56} \color{blue}{-48x} & = & \color{red}{48x} +15 \color{blue}{-48x} \color{blue}{+56} \\\Leftrightarrow & -126x-48x& = & 15+56 \\\Leftrightarrow & \color{red}{-174} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-174} & & \\\Leftrightarrow & x = \frac{-71}{174} & & \\ & V = \left\{ \frac{-71}{174} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{50x} +35 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{-24} \\\Leftrightarrow & 120x-50x& = & 35-24 \\\Leftrightarrow & \color{red}{70} x& = & 11 \\\Leftrightarrow & x = \frac{11}{70} & & \\ & V = \left\{ \frac{11}{70} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{2}{5})& = & -8x+\frac{8}{3} \\\Leftrightarrow & 15x+\frac{6}{5}& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{225}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 225x \color{red}{+18} & = & \color{red}{-120x} +40 \\\Leftrightarrow & 225x \color{red}{+18} \color{blue}{-18} \color{blue}{+120x} & = & \color{red}{-120x} +40 \color{blue}{+120x} \color{blue}{-18} \\\Leftrightarrow & 225x+120x& = & 40-18 \\\Leftrightarrow & \color{red}{345} x& = & 22 \\\Leftrightarrow & x = \frac{22}{345} & & \\ & V = \left\{ \frac{22}{345} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x+\frac{2}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 8x+\frac{8}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 24x \color{red}{+8} & = & \color{red}{9x} +8 \\\Leftrightarrow & 24x \color{red}{+8} \color{blue}{-8} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{-8} \\\Leftrightarrow & 24x-9x& = & 8-8 \\\Leftrightarrow & \color{red}{15} x& = & 0 \\\Leftrightarrow & x = \frac{0}{15} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)