Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{-1}& = &-14 \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1} & = &-14\color{blue}{+1} \\\Leftrightarrow &-10x & = &-13\\\Leftrightarrow & \color{red}{-10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-13}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-2}& = &13 \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &-8x & = &15\\\Leftrightarrow & \color{red}{-8}x & = &15\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{15}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{8} } & & \\ & V = \left\{ \frac{-15}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & 13x \color{red}{+11}& = &-12 \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11} & = &-12\color{blue}{-11} \\\Leftrightarrow &13x & = &-23\\\Leftrightarrow & \color{red}{13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-23}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{13} } & & \\ & V = \left\{ \frac{-23}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{-14}& = &-9 \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14} & = &-9\color{blue}{+14} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+12}& = &12 \\\Leftrightarrow & 2x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &2x & = &0\\\Leftrightarrow & \color{red}{2}x & = &0\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{0}{2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{+15}& = &2 \\\Leftrightarrow & 8x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-10}& = &-1 \\\Leftrightarrow & -5x \color{red}{-10}\color{blue}{+10} & = &-1\color{blue}{+10} \\\Leftrightarrow &-5x & = &9\\\Leftrightarrow & \color{red}{-5}x & = &9\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{9}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+8}& = &9 \\\Leftrightarrow & 7x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = &-3 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-3\color{blue}{-11} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+4}& = &-14 \\\Leftrightarrow & -4x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &-4x & = &-18\\\Leftrightarrow & \color{red}{-4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+15}& = &13 \\\Leftrightarrow & 5x \color{red}{+15}\color{blue}{-15} & = &13\color{blue}{-15} \\\Leftrightarrow &5x & = &-2\\\Leftrightarrow & \color{red}{5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-2}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-6}& = &15 \\\Leftrightarrow & 14x \color{red}{-6}\color{blue}{+6} & = &15\color{blue}{+6} \\\Leftrightarrow &14x & = &21\\\Leftrightarrow & \color{red}{14}x & = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)