Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & 7x+\frac{2}{9} \\\Leftrightarrow & -30x+\frac{12}{5}& = & 7x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-1350}{ \color{blue}{45} }x+ \frac{108}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -1350x \color{red}{+108} & = & \color{red}{315x} +10 \\\Leftrightarrow & -1350x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & -1350x-315x& = & 10-108 \\\Leftrightarrow & \color{red}{-1665} x& = & -98 \\\Leftrightarrow & x = \frac{-98}{-1665} & & \\\Leftrightarrow & x = \frac{98}{1665} & & \\ & V = \left\{ \frac{98}{1665} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{2}{7})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -20x+\frac{10}{7}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} })& = & (\frac{42}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+20} & = & \color{red}{42x} +63 \\\Leftrightarrow & -280x \color{red}{+20} \color{blue}{-20} \color{blue}{-42x} & = & \color{red}{42x} +63 \color{blue}{-42x} \color{blue}{-20} \\\Leftrightarrow & -280x-42x& = & 63-20 \\\Leftrightarrow & \color{red}{-322} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-322} & & \\\Leftrightarrow & x = \frac{-43}{322} & & \\ & V = \left\{ \frac{-43}{322} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{3}{4})& = & -7x+\frac{7}{2} \\\Leftrightarrow & 15x+\frac{15}{4}& = & -7x+\frac{7}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{14}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 60x \color{red}{+15} & = & \color{red}{-28x} +14 \\\Leftrightarrow & 60x \color{red}{+15} \color{blue}{-15} \color{blue}{+28x} & = & \color{red}{-28x} +14 \color{blue}{+28x} \color{blue}{-15} \\\Leftrightarrow & 60x+28x& = & 14-15 \\\Leftrightarrow & \color{red}{88} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{88} & & \\ & V = \left\{ \frac{-1}{88} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-300}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -300x \color{red}{+24} & = & \color{red}{-70x} +45 \\\Leftrightarrow & -300x \color{red}{+24} \color{blue}{-24} \color{blue}{+70x} & = & \color{red}{-70x} +45 \color{blue}{+70x} \color{blue}{-24} \\\Leftrightarrow & -300x+70x& = & 45-24 \\\Leftrightarrow & \color{red}{-230} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-230} & & \\\Leftrightarrow & x = \frac{-21}{230} & & \\ & V = \left\{ \frac{-21}{230} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{5}{9})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 16x-\frac{20}{9}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1008}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1008x \color{red}{-140} & = & \color{red}{-189x} +18 \\\Leftrightarrow & 1008x \color{red}{-140} \color{blue}{+140} \color{blue}{+189x} & = & \color{red}{-189x} +18 \color{blue}{+189x} \color{blue}{+140} \\\Leftrightarrow & 1008x+189x& = & 18+140 \\\Leftrightarrow & \color{red}{1197} x& = & 158 \\\Leftrightarrow & x = \frac{158}{1197} & & \\ & V = \left\{ \frac{158}{1197} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{9})& = & -7x+\frac{10}{11} \\\Leftrightarrow & 10x-\frac{25}{9}& = & -7x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x- \frac{275}{ \color{blue}{99} })& = & (\frac{-693}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{-275} & = & \color{red}{-693x} +90 \\\Leftrightarrow & 990x \color{red}{-275} \color{blue}{+275} \color{blue}{+693x} & = & \color{red}{-693x} +90 \color{blue}{+693x} \color{blue}{+275} \\\Leftrightarrow & 990x+693x& = & 90+275 \\\Leftrightarrow & \color{red}{1683} x& = & 365 \\\Leftrightarrow & x = \frac{365}{1683} & & \\ & V = \left\{ \frac{365}{1683} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{11})& = & -4x+\frac{8}{3} \\\Leftrightarrow & 35x+\frac{35}{11}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{1155}{ \color{blue}{33} }x+ \frac{105}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 1155x \color{red}{+105} & = & \color{red}{-132x} +88 \\\Leftrightarrow & 1155x \color{red}{+105} \color{blue}{-105} \color{blue}{+132x} & = & \color{red}{-132x} +88 \color{blue}{+132x} \color{blue}{-105} \\\Leftrightarrow & 1155x+132x& = & 88-105 \\\Leftrightarrow & \color{red}{1287} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{1287} & & \\ & V = \left\{ \frac{-17}{1287} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{3}{4})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{16}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-45} & = & \color{red}{-24x} +16 \\\Leftrightarrow & 180x \color{red}{-45} \color{blue}{+45} \color{blue}{+24x} & = & \color{red}{-24x} +16 \color{blue}{+24x} \color{blue}{+45} \\\Leftrightarrow & 180x+24x& = & 16+45 \\\Leftrightarrow & \color{red}{204} x& = & 61 \\\Leftrightarrow & x = \frac{61}{204} & & \\ & V = \left\{ \frac{61}{204} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{5}{3})& = & -5x+\frac{9}{8} \\\Leftrightarrow & -12x-\frac{20}{3}& = & -5x+\frac{9}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x- \frac{160}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{27}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{-160} & = & \color{red}{-120x} +27 \\\Leftrightarrow & -288x \color{red}{-160} \color{blue}{+160} \color{blue}{+120x} & = & \color{red}{-120x} +27 \color{blue}{+120x} \color{blue}{+160} \\\Leftrightarrow & -288x+120x& = & 27+160 \\\Leftrightarrow & \color{red}{-168} x& = & 187 \\\Leftrightarrow & x = \frac{187}{-168} & & \\\Leftrightarrow & x = \frac{-187}{168} & & \\ & V = \left\{ \frac{-187}{168} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x-\frac{5}{4})& = & 2x+\frac{7}{10} \\\Leftrightarrow & 9x+\frac{15}{4}& = & 2x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{180}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{40}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 180x \color{red}{+75} & = & \color{red}{40x} +14 \\\Leftrightarrow & 180x \color{red}{+75} \color{blue}{-75} \color{blue}{-40x} & = & \color{red}{40x} +14 \color{blue}{-40x} \color{blue}{-75} \\\Leftrightarrow & 180x-40x& = & 14-75 \\\Leftrightarrow & \color{red}{140} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{140} & & \\ & V = \left\{ \frac{-61}{140} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{2}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 6x+\frac{4}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+8} & = & \color{red}{50x} +45 \\\Leftrightarrow & 60x \color{red}{+8} \color{blue}{-8} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{-8} \\\Leftrightarrow & 60x-50x& = & 45-8 \\\Leftrightarrow & \color{red}{10} x& = & 37 \\\Leftrightarrow & x = \frac{37}{10} & & \\ & V = \left\{ \frac{37}{10} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{3}{4})& = & -4x+\frac{9}{7} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{9}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{36}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{-105} & = & \color{red}{-112x} +36 \\\Leftrightarrow & -420x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +36 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & -420x+112x& = & 36+105 \\\Leftrightarrow & \color{red}{-308} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-308} & & \\\Leftrightarrow & x = \frac{-141}{308} & & \\ & V = \left\{ \frac{-141}{308} \right\} & \\\end{align}\)