Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+13}& = &9 \\\Leftrightarrow & -8x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+2}& = &-2 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &-2\color{blue}{-2} \\\Leftrightarrow &4x & = &-4\\\Leftrightarrow & \color{red}{4}x & = &-4\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-4}{4} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & -10x \color{red}{+9}& = &-6 \\\Leftrightarrow & -10x \color{red}{+9}\color{blue}{-9} & = &-6\color{blue}{-9} \\\Leftrightarrow &-10x & = &-15\\\Leftrightarrow & \color{red}{-10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{-14}& = &-1 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &-1\color{blue}{+14} \\\Leftrightarrow &-2x & = &13\\\Leftrightarrow & \color{red}{-2}x & = &13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-6}& = &-15 \\\Leftrightarrow & 11x \color{red}{-6}\color{blue}{+6} & = &-15\color{blue}{+6} \\\Leftrightarrow &11x & = &-9\\\Leftrightarrow & \color{red}{11}x & = &-9\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-9}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{11} } & & \\ & V = \left\{ \frac{-9}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -4x \color{red}{+2}& = &15 \\\Leftrightarrow & -4x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-7}& = &-7 \\\Leftrightarrow & -8x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-11}& = &7 \\\Leftrightarrow & 5x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &5x & = &18\\\Leftrightarrow & \color{red}{5}x & = &18\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{18}{5} \\\Leftrightarrow & \color{green}{ x = \frac{18}{5} } & & \\ & V = \left\{ \frac{18}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-14}& = &-11 \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-3}& = &-7 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &-7\color{blue}{+3} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -11x \color{red}{+8}& = &7 \\\Leftrightarrow & -11x \color{red}{+8}\color{blue}{-8} & = &7\color{blue}{-8} \\\Leftrightarrow &-11x & = &-1\\\Leftrightarrow & \color{red}{-11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{1}{11} } & & \\ & V = \left\{ \frac{1}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+5}& = &-11 \\\Leftrightarrow & -6x \color{red}{+5}\color{blue}{-5} & = &-11\color{blue}{-5} \\\Leftrightarrow &-6x & = &-16\\\Leftrightarrow & \color{red}{-6}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-16}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)