Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-14}& = &4 \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14} & = &4\color{blue}{+14} \\\Leftrightarrow &-10x & = &18\\\Leftrightarrow & \color{red}{-10}x & = &18\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{18}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-13}& = &13 \\\Leftrightarrow & 4x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &4x & = &26\\\Leftrightarrow & \color{red}{4}x & = &26\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{26}{4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{2} } & & \\ & V = \left\{ \frac{13}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+3}& = &-12 \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3} & = &-12\color{blue}{-3} \\\Leftrightarrow &-10x & = &-15\\\Leftrightarrow & \color{red}{-10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -15x \color{red}{-14}& = &9 \\\Leftrightarrow & -15x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &-15x & = &23\\\Leftrightarrow & \color{red}{-15}x & = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+3}& = &6 \\\Leftrightarrow & -14x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-12}& = &-1 \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12} & = &-1\color{blue}{+12} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+7}& = &-6 \\\Leftrightarrow & -7x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-12}& = &5 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &4x & = &17\\\Leftrightarrow & \color{red}{4}x & = &17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-11}& = &8 \\\Leftrightarrow & -2x \color{red}{-11}\color{blue}{+11} & = &8\color{blue}{+11} \\\Leftrightarrow &-2x & = &19\\\Leftrightarrow & \color{red}{-2}x & = &19\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{19}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{2} } & & \\ & V = \left\{ \frac{-19}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{-2}& = &8 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-11}& = &-2 \\\Leftrightarrow & 4x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &4x & = &9\\\Leftrightarrow & \color{red}{4}x & = &9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+6}& = &2 \\\Leftrightarrow & -11x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)