Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-4}& = &15 \\\Leftrightarrow & 7x \color{red}{-4}\color{blue}{+4} & = &15\color{blue}{+4} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-4}& = &1 \\\Leftrightarrow & 12x \color{red}{-4}\color{blue}{+4} & = &1\color{blue}{+4} \\\Leftrightarrow &12x & = &5\\\Leftrightarrow & \color{red}{12}x & = &5\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{5}{12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{-11}& = &14 \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &-15x & = &25\\\Leftrightarrow & \color{red}{-15}x & = &25\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{25}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{+2}& = &3 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -15x \color{red}{-5}& = &9 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &9\color{blue}{+5} \\\Leftrightarrow &-15x & = &14\\\Leftrightarrow & \color{red}{-15}x & = &14\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{14}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{+10}& = &7 \\\Leftrightarrow & -11x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+4}& = &-11 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &12x & = &-15\\\Leftrightarrow & \color{red}{12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-15}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+1}& = &-10 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &-10\color{blue}{-1} \\\Leftrightarrow &-14x & = &-11\\\Leftrightarrow & \color{red}{-14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-11}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{11}{14} } & & \\ & V = \left\{ \frac{11}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-8}& = &7 \\\Leftrightarrow & -10x \color{red}{-8}\color{blue}{+8} & = &7\color{blue}{+8} \\\Leftrightarrow &-10x & = &15\\\Leftrightarrow & \color{red}{-10}x & = &15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-13}& = &-5 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &-5\color{blue}{+13} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 14x \color{red}{+8}& = &10 \\\Leftrightarrow & 14x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &14x & = &2\\\Leftrightarrow & \color{red}{14}x & = &2\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{2}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{+4}& = &-15 \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4} & = &-15\color{blue}{-4} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)