Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -x \color{red}{+1}& = &-11 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-11\color{blue}{-1} \\\Leftrightarrow &-x & = &-12\\\Leftrightarrow & \color{red}{-}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-12}{-1} \\\Leftrightarrow & \color{green}{ x = 12 } & & \\ & V = \left\{ 12 \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-4}& = &11 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &11\color{blue}{+4} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -15x \color{red}{+15}& = &15 \\\Leftrightarrow & -15x \color{red}{+15}\color{blue}{-15} & = &15\color{blue}{-15} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+1}& = &8 \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1} & = &8\color{blue}{-1} \\\Leftrightarrow &-2x & = &7\\\Leftrightarrow & \color{red}{-2}x & = &7\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{7}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{-5}& = &1 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &1\color{blue}{+5} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+11}& = &-8 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &-10x & = &-19\\\Leftrightarrow & \color{red}{-10}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+4}& = &10 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &-2x & = &6\\\Leftrightarrow & \color{red}{-2}x & = &6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{6}{-2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+11}& = &14 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &14\color{blue}{-11} \\\Leftrightarrow &4x & = &3\\\Leftrightarrow & \color{red}{4}x & = &3\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{3}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+9}& = &-2 \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9} & = &-2\color{blue}{-9} \\\Leftrightarrow &-3x & = &-11\\\Leftrightarrow & \color{red}{-3}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{11}{3} } & & \\ & V = \left\{ \frac{11}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-8}& = &5 \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+12}& = &-10 \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12} & = &-10\color{blue}{-12} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = &3 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &3\color{blue}{+3} \\\Leftrightarrow &-13x & = &6\\\Leftrightarrow & \color{red}{-13}x & = &6\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{6}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)