Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

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