Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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