Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{-13}& = &8 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &-4x & = &21\\\Leftrightarrow & \color{red}{-4}x & = &21\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{21}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{4} } & & \\ & V = \left\{ \frac{-21}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+7}& = &4 \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7} & = &4\color{blue}{-7} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+3}& = &2 \\\Leftrightarrow & -15x \color{red}{+3}\color{blue}{-3} & = &2\color{blue}{-3} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{+5}& = &15 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &15\color{blue}{-5} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+7}& = &-13 \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7} & = &-13\color{blue}{-7} \\\Leftrightarrow &-x & = &-20\\\Leftrightarrow & \color{red}{-}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-20}{-1} \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-7}& = &6 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &6\color{blue}{+7} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-1}& = &6 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-9}& = &9 \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9} & = &9\color{blue}{+9} \\\Leftrightarrow &-12x & = &18\\\Leftrightarrow & \color{red}{-12}x & = &18\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{18}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -13x \color{red}{-6}& = &6 \\\Leftrightarrow & -13x \color{red}{-6}\color{blue}{+6} & = &6\color{blue}{+6} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+15}& = &-7 \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15} & = &-7\color{blue}{-15} \\\Leftrightarrow &-x & = &-22\\\Leftrightarrow & \color{red}{-}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-22}{-1} \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{-11}& = &6 \\\Leftrightarrow & -6x \color{red}{-11}\color{blue}{+11} & = &6\color{blue}{+11} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{-10}& = &13 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &13\color{blue}{+10} \\\Leftrightarrow &-6x & = &23\\\Leftrightarrow & \color{red}{-6}x & = &23\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{23}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{6} } & & \\ & V = \left\{ \frac{-23}{6} \right\} & \\\end{align}\)