Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{6}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-66} & = & \color{red}{275x} +10 \\\Leftrightarrow & -495x \color{red}{-66} \color{blue}{+66} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+66} \\\Leftrightarrow & -495x-275x& = & 10+66 \\\Leftrightarrow & \color{red}{-770} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-770} & & \\\Leftrightarrow & x = \frac{-38}{385} & & \\ & V = \left\{ \frac{-38}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{396}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{-220}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 396x \color{red}{-165} & = & \color{red}{-220x} +12 \\\Leftrightarrow & 396x \color{red}{-165} \color{blue}{+165} \color{blue}{+220x} & = & \color{red}{-220x} +12 \color{blue}{+220x} \color{blue}{+165} \\\Leftrightarrow & 396x+220x& = & 12+165 \\\Leftrightarrow & \color{red}{616} x& = & 177 \\\Leftrightarrow & x = \frac{177}{616} & & \\ & V = \left\{ \frac{177}{616} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{4}{5})& = & -5x+\frac{7}{4} \\\Leftrightarrow & -12x-\frac{12}{5}& = & -5x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-240}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-100}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -240x \color{red}{-48} & = & \color{red}{-100x} +35 \\\Leftrightarrow & -240x \color{red}{-48} \color{blue}{+48} \color{blue}{+100x} & = & \color{red}{-100x} +35 \color{blue}{+100x} \color{blue}{+48} \\\Leftrightarrow & -240x+100x& = & 35+48 \\\Leftrightarrow & \color{red}{-140} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-140} & & \\\Leftrightarrow & x = \frac{-83}{140} & & \\ & V = \left\{ \frac{-83}{140} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{2}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -4x-\frac{4}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-40}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -40x \color{red}{-8} & = & \color{red}{50x} +35 \\\Leftrightarrow & -40x \color{red}{-8} \color{blue}{+8} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{+8} \\\Leftrightarrow & -40x-50x& = & 35+8 \\\Leftrightarrow & \color{red}{-90} x& = & 43 \\\Leftrightarrow & x = \frac{43}{-90} & & \\\Leftrightarrow & x = \frac{-43}{90} & & \\ & V = \left\{ \frac{-43}{90} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 4x-\frac{4}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-4} & = & \color{red}{35x} +4 \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+4} \\\Leftrightarrow & 20x-35x& = & 4+4 \\\Leftrightarrow & \color{red}{-15} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-15} & & \\\Leftrightarrow & x = \frac{-8}{15} & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{5}{7})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-350}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -350x \color{red}{-50} & = & \color{red}{-245x} +56 \\\Leftrightarrow & -350x \color{red}{-50} \color{blue}{+50} \color{blue}{+245x} & = & \color{red}{-245x} +56 \color{blue}{+245x} \color{blue}{+50} \\\Leftrightarrow & -350x+245x& = & 56+50 \\\Leftrightarrow & \color{red}{-105} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-105} & & \\\Leftrightarrow & x = \frac{-106}{105} & & \\ & V = \left\{ \frac{-106}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{+8} & = & \color{red}{45x} +24 \\\Leftrightarrow & 54x \color{red}{+8} \color{blue}{-8} \color{blue}{-45x} & = & \color{red}{45x} +24 \color{blue}{-45x} \color{blue}{-8} \\\Leftrightarrow & 54x-45x& = & 24-8 \\\Leftrightarrow & \color{red}{9} x& = & 16 \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{7})& = & -9x+\frac{5}{7} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+10} & = & \color{red}{-63x} +5 \\\Leftrightarrow & -28x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +5 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & -28x+63x& = & 5-10 \\\Leftrightarrow & \color{red}{35} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{35} & & \\\Leftrightarrow & x = \frac{-1}{7} & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{9})& = & 9x+\frac{10}{9} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 9x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{81x} +10 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-81x} & = & \color{red}{81x} +10 \color{blue}{-81x} \color{blue}{-8} \\\Leftrightarrow & 180x-81x& = & 10-8 \\\Leftrightarrow & \color{red}{99} x& = & 2 \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{3}{10})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -28x+\frac{21}{10}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 10 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-280}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -280x \color{red}{+21} & = & \color{red}{30x} +45 \\\Leftrightarrow & -280x \color{red}{+21} \color{blue}{-21} \color{blue}{-30x} & = & \color{red}{30x} +45 \color{blue}{-30x} \color{blue}{-21} \\\Leftrightarrow & -280x-30x& = & 45-21 \\\Leftrightarrow & \color{red}{-310} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-310} & & \\\Leftrightarrow & x = \frac{-12}{155} & & \\ & V = \left\{ \frac{-12}{155} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-36}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -36x \color{red}{+16} & = & \color{red}{-15x} +4 \\\Leftrightarrow & -36x \color{red}{+16} \color{blue}{-16} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{-16} \\\Leftrightarrow & -36x+15x& = & 4-16 \\\Leftrightarrow & \color{red}{-21} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-21} & & \\\Leftrightarrow & x = \frac{4}{7} & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{4}{11})& = & -4x+\frac{2}{11} \\\Leftrightarrow & -15x-\frac{12}{11}& = & -4x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{12}{ \color{blue}{11} })& = & (\frac{-44}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-12} & = & \color{red}{-44x} +2 \\\Leftrightarrow & -165x \color{red}{-12} \color{blue}{+12} \color{blue}{+44x} & = & \color{red}{-44x} +2 \color{blue}{+44x} \color{blue}{+12} \\\Leftrightarrow & -165x+44x& = & 2+12 \\\Leftrightarrow & \color{red}{-121} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-121} & & \\\Leftrightarrow & x = \frac{-14}{121} & & \\ & V = \left\{ \frac{-14}{121} \right\} & \\\end{align}\)