Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{-7}& = &15 \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7} & = &15\color{blue}{+7} \\\Leftrightarrow &-9x & = &22\\\Leftrightarrow & \color{red}{-9}x & = &22\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{22}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{9} } & & \\ & V = \left\{ \frac{-22}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-13}& = &-13 \\\Leftrightarrow & -4x \color{red}{-13}\color{blue}{+13} & = &-13\color{blue}{+13} \\\Leftrightarrow &-4x & = &0\\\Leftrightarrow & \color{red}{-4}x & = &0\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{0}{-4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+4}& = &5 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &5\color{blue}{-4} \\\Leftrightarrow &-2x & = &1\\\Leftrightarrow & \color{red}{-2}x & = &1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{-13}& = &8 \\\Leftrightarrow & 14x \color{red}{-13}\color{blue}{+13} & = &8\color{blue}{+13} \\\Leftrightarrow &14x & = &21\\\Leftrightarrow & \color{red}{14}x & = &21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -10x \color{red}{+1}& = &1 \\\Leftrightarrow & -10x \color{red}{+1}\color{blue}{-1} & = &1\color{blue}{-1} \\\Leftrightarrow &-10x & = &0\\\Leftrightarrow & \color{red}{-10}x & = &0\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{0}{-10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-10}& = &1 \\\Leftrightarrow & -10x \color{red}{-10}\color{blue}{+10} & = &1\color{blue}{+10} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{-11}& = &3 \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11} & = &3\color{blue}{+11} \\\Leftrightarrow &-10x & = &14\\\Leftrightarrow & \color{red}{-10}x & = &14\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{14}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{5} } & & \\ & V = \left\{ \frac{-7}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+3}& = &-3 \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3} & = &-3\color{blue}{-3} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-15}& = &-15 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+1}& = &5 \\\Leftrightarrow & 9x \color{red}{+1}\color{blue}{-1} & = &5\color{blue}{-1} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+12}& = &-11 \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12} & = &-11\color{blue}{-12} \\\Leftrightarrow &-2x & = &-23\\\Leftrightarrow & \color{red}{-2}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-23}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{23}{2} } & & \\ & V = \left\{ \frac{23}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-13}& = &11 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &8x & = &24\\\Leftrightarrow & \color{red}{8}x & = &24\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{24}{8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)