Vgln. eerste graad (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bepaal de waarde van x.

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

---

Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{-9}& = &14 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &14\color{blue}{+9} \\\Leftrightarrow &7x & = &23\\\Leftrightarrow & \color{red}{7}x & = &23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{23}{7} } & & \\ & V = \left\{ \frac{23}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{+10}& = &-3 \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10} & = &-3\color{blue}{-10} \\\Leftrightarrow &-7x & = &-13\\\Leftrightarrow & \color{red}{-7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-13}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{-1}& = &-3 \\\Leftrightarrow & -x \color{red}{-1}\color{blue}{+1} & = &-3\color{blue}{+1} \\\Leftrightarrow &-x & = &-2\\\Leftrightarrow & \color{red}{-}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-2}{-1} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+10}& = &-11 \\\Leftrightarrow & -7x \color{red}{+10}\color{blue}{-10} & = &-11\color{blue}{-10} \\\Leftrightarrow &-7x & = &-21\\\Leftrightarrow & \color{red}{-7}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-21}{-7} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-7}& = &8 \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7} & = &8\color{blue}{+7} \\\Leftrightarrow &2x & = &15\\\Leftrightarrow & \color{red}{2}x & = &15\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{15}{2} \\\Leftrightarrow & \color{green}{ x = \frac{15}{2} } & & \\ & V = \left\{ \frac{15}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 12x \color{red}{+2}& = &5 \\\Leftrightarrow & 12x \color{red}{+2}\color{blue}{-2} & = &5\color{blue}{-2} \\\Leftrightarrow &12x & = &3\\\Leftrightarrow & \color{red}{12}x & = &3\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{3}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-15}& = &2 \\\Leftrightarrow & -11x \color{red}{-15}\color{blue}{+15} & = &2\color{blue}{+15} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+8}& = &9 \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &4x & = &1\\\Leftrightarrow & \color{red}{4}x & = &1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{4} } & & \\ & V = \left\{ \frac{1}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{-2}& = &-14 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &7x & = &-12\\\Leftrightarrow & \color{red}{7}x & = &-12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{+13}& = &10 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &10\color{blue}{-13} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{-13}& = &-1 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &-1\color{blue}{+13} \\\Leftrightarrow &2x & = &12\\\Leftrightarrow & \color{red}{2}x & = &12\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{12}{2} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+7}& = &15 \\\Leftrightarrow & -6x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)