Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+15}& = &-13 \\\Leftrightarrow & -5x \color{red}{+15}\color{blue}{-15} & = &-13\color{blue}{-15} \\\Leftrightarrow &-5x & = &-28\\\Leftrightarrow & \color{red}{-5}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-28}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{28}{5} } & & \\ & V = \left\{ \frac{28}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 7x \color{red}{+4}& = &10 \\\Leftrightarrow & 7x \color{red}{+4}\color{blue}{-4} & = &10\color{blue}{-4} \\\Leftrightarrow &7x & = &6\\\Leftrightarrow & \color{red}{7}x & = &6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-15}& = &-14 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &-14\color{blue}{+15} \\\Leftrightarrow &2x & = &1\\\Leftrightarrow & \color{red}{2}x & = &1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+9}& = &-2 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &-2\color{blue}{-9} \\\Leftrightarrow &4x & = &-11\\\Leftrightarrow & \color{red}{4}x & = &-11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{4} } & & \\ & V = \left\{ \frac{-11}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+2}& = &-5 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &-5\color{blue}{-2} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-12}& = &-10 \\\Leftrightarrow & -13x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+3}& = &15 \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &-13x & = &12\\\Leftrightarrow & \color{red}{-13}x & = &12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-1}& = &6 \\\Leftrightarrow & 9x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &9x & = &7\\\Leftrightarrow & \color{red}{9}x & = &7\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{7}{9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-1}& = &-5 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &-4x & = &-4\\\Leftrightarrow & \color{red}{-4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-4}{-4} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+5}& = &-5 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &-5\color{blue}{-5} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{+14}& = &10 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &10\color{blue}{-14} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-7}& = &13 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &6x & = &20\\\Leftrightarrow & \color{red}{6}x & = &20\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{20}{6} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)