Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+10}& = &-3 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &-3\color{blue}{-10} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -13x \color{red}{+15}& = &-10 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &-10\color{blue}{-15} \\\Leftrightarrow &-13x & = &-25\\\Leftrightarrow & \color{red}{-13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-25}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{25}{13} } & & \\ & V = \left\{ \frac{25}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+13}& = &-3 \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &-5x & = &-16\\\Leftrightarrow & \color{red}{-5}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-12}& = &-3 \\\Leftrightarrow & -14x \color{red}{-12}\color{blue}{+12} & = &-3\color{blue}{+12} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-6}& = &-9 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &-9\color{blue}{+6} \\\Leftrightarrow &-3x & = &-3\\\Leftrightarrow & \color{red}{-3}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-3}{-3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-9}& = &12 \\\Leftrightarrow & 10x \color{red}{-9}\color{blue}{+9} & = &12\color{blue}{+9} \\\Leftrightarrow &10x & = &21\\\Leftrightarrow & \color{red}{10}x & = &21\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{21}{10} \\\Leftrightarrow & \color{green}{ x = \frac{21}{10} } & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 5x \color{red}{-8}& = &-4 \\\Leftrightarrow & 5x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &5x & = &4\\\Leftrightarrow & \color{red}{5}x & = &4\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{4}{5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-12}& = &-14 \\\Leftrightarrow & 14x \color{red}{-12}\color{blue}{+12} & = &-14\color{blue}{+12} \\\Leftrightarrow &14x & = &-2\\\Leftrightarrow & \color{red}{14}x & = &-2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+9}& = &-14 \\\Leftrightarrow & 7x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{-3}& = &-10 \\\Leftrightarrow & -15x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &-15x & = &-7\\\Leftrightarrow & \color{red}{-15}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-7}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+3}& = &13 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &13\color{blue}{-3} \\\Leftrightarrow &-x & = &10\\\Leftrightarrow & \color{red}{-}x & = &10\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{10}{-1} \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-15}& = &-11 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)