Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

1. \(10x+2=-1\)
2. \(6x-6=15\)
3. \(-11x+15=7\)
4. \(-3x+1=6\)
5. \(-2x-12=8\)
6. \(x+13=2\)
7. \(-10x+5=-6\)
8. \(9x+14=-14\)
9. \(15x+13=-12\)
10. \(-15x+4=-14\)
11. \(6x-15=14\)
12. \(-11x-3=-10\)

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+2}& = &-1 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-1\color{blue}{-2} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-6}& = &15 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &15\color{blue}{+6} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{+15}& = &7 \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15} & = &7\color{blue}{-15} \\\Leftrightarrow &-11x & = &-8\\\Leftrightarrow & \color{red}{-11}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-8}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{8}{11} } & & \\ & V = \left\{ \frac{8}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+1}& = &6 \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1} & = &6\color{blue}{-1} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-12}& = &8 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &-2x & = &20\\\Leftrightarrow & \color{red}{-2}x & = &20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{20}{-2} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+13}& = &2 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &2\color{blue}{-13} \\\Leftrightarrow &x & = &-11\\\Leftrightarrow & \color{red}{}x & = &-11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -11 \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+5}& = &-6 \\\Leftrightarrow & -10x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &-10x & = &-11\\\Leftrightarrow & \color{red}{-10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{11}{10} } & & \\ & V = \left\{ \frac{11}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+14}& = &-14 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &9x & = &-28\\\Leftrightarrow & \color{red}{9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-28}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{9} } & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+13}& = &-12 \\\Leftrightarrow & 15x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &15x & = &-25\\\Leftrightarrow & \color{red}{15}x & = &-25\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-25}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+4}& = &-14 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &-15x & = &-18\\\Leftrightarrow & \color{red}{-15}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-18}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-15}& = &14 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &6x & = &29\\\Leftrightarrow & \color{red}{6}x & = &29\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{29}{6} \\\Leftrightarrow & \color{green}{ x = \frac{29}{6} } & & \\ & V = \left\{ \frac{29}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-3}& = &-10 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &-11x & = &-7\\\Leftrightarrow & \color{red}{-11}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-7}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)