Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{-12}& = &5 \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+3}& = &-6 \\\Leftrightarrow & -12x \color{red}{+3}\color{blue}{-3} & = &-6\color{blue}{-3} \\\Leftrightarrow &-12x & = &-9\\\Leftrightarrow & \color{red}{-12}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+9}& = &15 \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9} & = &15\color{blue}{-9} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-13}& = &13 \\\Leftrightarrow & -15x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &-15x & = &26\\\Leftrightarrow & \color{red}{-15}x & = &26\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{26}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{15} } & & \\ & V = \left\{ \frac{-26}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{-14}& = &-1 \\\Leftrightarrow & -5x \color{red}{-14}\color{blue}{+14} & = &-1\color{blue}{+14} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+2}& = &-3 \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2} & = &-3\color{blue}{-2} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-8}& = &9 \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8} & = &9\color{blue}{+8} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{+12}& = &11 \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12} & = &11\color{blue}{-12} \\\Leftrightarrow &-2x & = &-1\\\Leftrightarrow & \color{red}{-2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{+8}& = &5 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &5\color{blue}{-8} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{-14}& = &-10 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &-10\color{blue}{+14} \\\Leftrightarrow &x & = &4\\\Leftrightarrow & \color{red}{}x & = &4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 4 \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-5}& = &12 \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5} & = &12\color{blue}{+5} \\\Leftrightarrow &2x & = &17\\\Leftrightarrow & \color{red}{2}x & = &17\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{17}{2} \\\Leftrightarrow & \color{green}{ x = \frac{17}{2} } & & \\ & V = \left\{ \frac{17}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+2}& = &7 \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2} & = &7\color{blue}{-2} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)