Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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