Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+3}& = &14 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &11x & = &11\\\Leftrightarrow & \color{red}{11}x & = &11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{11}{11} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+8}& = &-2 \\\Leftrightarrow & -15x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &-15x & = &-10\\\Leftrightarrow & \color{red}{-15}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{+4}& = &-9 \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-3}& = &-4 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-6}& = &-1 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &-1\color{blue}{+6} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -11x \color{red}{-1}& = &4 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &4\color{blue}{+1} \\\Leftrightarrow &-11x & = &5\\\Leftrightarrow & \color{red}{-11}x & = &5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{11} } & & \\ & V = \left\{ \frac{-5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+4}& = &2 \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4} & = &2\color{blue}{-4} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-11}& = &2 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &2\color{blue}{+11} \\\Leftrightarrow &-5x & = &13\\\Leftrightarrow & \color{red}{-5}x & = &13\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{13}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{5} } & & \\ & V = \left\{ \frac{-13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+13}& = &13 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+3}& = &-9 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &-9\color{blue}{-3} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-7}& = &3 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &-10x & = &10\\\Leftrightarrow & \color{red}{-10}x & = &10\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{10}{-10} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-2}& = &-14 \\\Leftrightarrow & 3x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &3x & = &-12\\\Leftrightarrow & \color{red}{3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-12}{3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)