Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & 7x+\frac{5}{6} \\\Leftrightarrow & -10x-\frac{10}{7}& = & 7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-420}{ \color{blue}{42} }x- \frac{60}{ \color{blue}{42} })& = & (\frac{294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{294x} +35 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{-294x} & = & \color{red}{294x} +35 \color{blue}{-294x} \color{blue}{+60} \\\Leftrightarrow & -420x-294x& = & 35+60 \\\Leftrightarrow & \color{red}{-714} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-714} & & \\\Leftrightarrow & x = \frac{-95}{714} & & \\ & V = \left\{ \frac{-95}{714} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{4}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+4} & = & \color{red}{77x} +6 \\\Leftrightarrow & -66x \color{red}{+4} \color{blue}{-4} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{-4} \\\Leftrightarrow & -66x-77x& = & 6-4 \\\Leftrightarrow & \color{red}{-143} x& = & 2 \\\Leftrightarrow & x = \frac{2}{-143} & & \\\Leftrightarrow & x = \frac{-2}{143} & & \\ & V = \left\{ \frac{-2}{143} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{3}{5})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 10x-\frac{6}{5}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{150}{ \color{blue}{15} }x- \frac{18}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 150x \color{red}{-18} & = & \color{red}{-105x} +10 \\\Leftrightarrow & 150x \color{red}{-18} \color{blue}{+18} \color{blue}{+105x} & = & \color{red}{-105x} +10 \color{blue}{+105x} \color{blue}{+18} \\\Leftrightarrow & 150x+105x& = & 10+18 \\\Leftrightarrow & \color{red}{255} x& = & 28 \\\Leftrightarrow & x = \frac{28}{255} & & \\ & V = \left\{ \frac{28}{255} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & 12x-\frac{18}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{-18} & = & \color{red}{-55x} +2 \\\Leftrightarrow & 132x \color{red}{-18} \color{blue}{+18} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{+18} \\\Leftrightarrow & 132x+55x& = & 2+18 \\\Leftrightarrow & \color{red}{187} x& = & 20 \\\Leftrightarrow & x = \frac{20}{187} & & \\ & V = \left\{ \frac{20}{187} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & -5x+\frac{10}{11} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -5x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{-220} & = & \color{red}{-165x} +30 \\\Leftrightarrow & 528x \color{red}{-220} \color{blue}{+220} \color{blue}{+165x} & = & \color{red}{-165x} +30 \color{blue}{+165x} \color{blue}{+220} \\\Leftrightarrow & 528x+165x& = & 30+220 \\\Leftrightarrow & \color{red}{693} x& = & 250 \\\Leftrightarrow & x = \frac{250}{693} & & \\ & V = \left\{ \frac{250}{693} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{2}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x+\frac{6}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{60}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 60x \color{red}{+6} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 60x \color{red}{+6} \color{blue}{-6} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-6} \\\Leftrightarrow & 60x+25x& = & 6-6 \\\Leftrightarrow & \color{red}{85} x& = & 0 \\\Leftrightarrow & x = \frac{0}{85} & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{5}{11})& = & -3x+\frac{5}{2} \\\Leftrightarrow & -14x-\frac{35}{11}& = & -3x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-308}{ \color{blue}{22} }x- \frac{70}{ \color{blue}{22} })& = & (\frac{-66}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -308x \color{red}{-70} & = & \color{red}{-66x} +55 \\\Leftrightarrow & -308x \color{red}{-70} \color{blue}{+70} \color{blue}{+66x} & = & \color{red}{-66x} +55 \color{blue}{+66x} \color{blue}{+70} \\\Leftrightarrow & -308x+66x& = & 55+70 \\\Leftrightarrow & \color{red}{-242} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-242} & & \\\Leftrightarrow & x = \frac{-125}{242} & & \\ & V = \left\{ \frac{-125}{242} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{9}{10} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{9}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-840}{ \color{blue}{70} }x- \frac{300}{ \color{blue}{70} })& = & (\frac{-350}{ \color{blue}{70} }x+ \frac{63}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -840x \color{red}{-300} & = & \color{red}{-350x} +63 \\\Leftrightarrow & -840x \color{red}{-300} \color{blue}{+300} \color{blue}{+350x} & = & \color{red}{-350x} +63 \color{blue}{+350x} \color{blue}{+300} \\\Leftrightarrow & -840x+350x& = & 63+300 \\\Leftrightarrow & \color{red}{-490} x& = & 363 \\\Leftrightarrow & x = \frac{363}{-490} & & \\\Leftrightarrow & x = \frac{-363}{490} & & \\ & V = \left\{ \frac{-363}{490} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{4}{3})& = & 3x+\frac{4}{5} \\\Leftrightarrow & 20x+\frac{16}{3}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{300}{ \color{blue}{15} }x+ \frac{80}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 300x \color{red}{+80} & = & \color{red}{45x} +12 \\\Leftrightarrow & 300x \color{red}{+80} \color{blue}{-80} \color{blue}{-45x} & = & \color{red}{45x} +12 \color{blue}{-45x} \color{blue}{-80} \\\Leftrightarrow & 300x-45x& = & 12-80 \\\Leftrightarrow & \color{red}{255} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{255} & & \\\Leftrightarrow & x = \frac{-4}{15} & & \\ & V = \left\{ \frac{-4}{15} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{4}{11})& = & 9x+\frac{8}{11} \\\Leftrightarrow & -4x-\frac{8}{11}& = & 9x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-44}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{99}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -44x \color{red}{-8} & = & \color{red}{99x} +8 \\\Leftrightarrow & -44x \color{red}{-8} \color{blue}{+8} \color{blue}{-99x} & = & \color{red}{99x} +8 \color{blue}{-99x} \color{blue}{+8} \\\Leftrightarrow & -44x-99x& = & 8+8 \\\Leftrightarrow & \color{red}{-143} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-143} & & \\\Leftrightarrow & x = \frac{-16}{143} & & \\ & V = \left\{ \frac{-16}{143} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{4}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 6x-\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{-24} & = & \color{red}{70x} +15 \\\Leftrightarrow & 60x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & 60x-70x& = & 15+24 \\\Leftrightarrow & \color{red}{-10} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-10} & & \\\Leftrightarrow & x = \frac{-39}{10} & & \\ & V = \left\{ \frac{-39}{10} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{3}{8})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 10x-\frac{15}{8}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{560}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 560x \color{red}{-105} & = & \color{red}{-392x} +80 \\\Leftrightarrow & 560x \color{red}{-105} \color{blue}{+105} \color{blue}{+392x} & = & \color{red}{-392x} +80 \color{blue}{+392x} \color{blue}{+105} \\\Leftrightarrow & 560x+392x& = & 80+105 \\\Leftrightarrow & \color{red}{952} x& = & 185 \\\Leftrightarrow & x = \frac{185}{952} & & \\ & V = \left\{ \frac{185}{952} \right\} & \\\end{align}\)