Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-2}& = &-6 \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{+9}& = &-1 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-1\color{blue}{-9} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-14}& = &2 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &2\color{blue}{+14} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{-13}& = &5 \\\Leftrightarrow & -11x \color{red}{-13}\color{blue}{+13} & = &5\color{blue}{+13} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-10}& = &15 \\\Leftrightarrow & 2x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &2x & = &25\\\Leftrightarrow & \color{red}{2}x & = &25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-11}& = &6 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &6\color{blue}{+11} \\\Leftrightarrow &3x & = &17\\\Leftrightarrow & \color{red}{3}x & = &17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{17}{3} } & & \\ & V = \left\{ \frac{17}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-1}& = &-7 \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1} & = &-7\color{blue}{+1} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+10}& = &-1 \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &9x & = &-11\\\Leftrightarrow & \color{red}{9}x & = &-11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{+14}& = &-4 \\\Leftrightarrow & 12x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &12x & = &-18\\\Leftrightarrow & \color{red}{12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-3}& = &3 \\\Leftrightarrow & -14x \color{red}{-3}\color{blue}{+3} & = &3\color{blue}{+3} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 6x \color{red}{-2}& = &5 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &5\color{blue}{+2} \\\Leftrightarrow &6x & = &7\\\Leftrightarrow & \color{red}{6}x & = &7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+12}& = &-8 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-8\color{blue}{-12} \\\Leftrightarrow &6x & = &-20\\\Leftrightarrow & \color{red}{6}x & = &-20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)