Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{-6}& = &14 \\\Leftrightarrow & 8x \color{red}{-6}\color{blue}{+6} & = &14\color{blue}{+6} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+10}& = &-12 \\\Leftrightarrow & 9x \color{red}{+10}\color{blue}{-10} & = &-12\color{blue}{-10} \\\Leftrightarrow &9x & = &-22\\\Leftrightarrow & \color{red}{9}x & = &-22\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-22}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+15}& = &-3 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &-3\color{blue}{-15} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+2}& = &13 \\\Leftrightarrow & -3x \color{red}{+2}\color{blue}{-2} & = &13\color{blue}{-2} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+4}& = &13 \\\Leftrightarrow & x \color{red}{+4}\color{blue}{-4} & = &13\color{blue}{-4} \\\Leftrightarrow &x & = &9\\\Leftrightarrow & \color{red}{}x & = &9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 9 \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+6}& = &-7 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &-7\color{blue}{-6} \\\Leftrightarrow &12x & = &-13\\\Leftrightarrow & \color{red}{12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-13}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-1}& = &-14 \\\Leftrightarrow & x \color{red}{-1}\color{blue}{+1} & = &-14\color{blue}{+1} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-12}& = &-2 \\\Leftrightarrow & -5x \color{red}{-12}\color{blue}{+12} & = &-2\color{blue}{+12} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{+1}& = &-12 \\\Leftrightarrow & 4x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &4x & = &-13\\\Leftrightarrow & \color{red}{4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-13}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{+9}& = &-3 \\\Leftrightarrow & -13x \color{red}{+9}\color{blue}{-9} & = &-3\color{blue}{-9} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-14}& = &-9 \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14} & = &-9\color{blue}{+14} \\\Leftrightarrow &10x & = &5\\\Leftrightarrow & \color{red}{10}x & = &5\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{5}{10} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{-14}& = &6 \\\Leftrightarrow & -10x \color{red}{-14}\color{blue}{+14} & = &6\color{blue}{+14} \\\Leftrightarrow &-10x & = &20\\\Leftrightarrow & \color{red}{-10}x & = &20\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{20}{-10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)