Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{+3}& = &-3 \\\Leftrightarrow & -2x \color{red}{+3}\color{blue}{-3} & = &-3\color{blue}{-3} \\\Leftrightarrow &-2x & = &-6\\\Leftrightarrow & \color{red}{-2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-6}{-2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-2}& = &15 \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2} & = &15\color{blue}{+2} \\\Leftrightarrow &-8x & = &17\\\Leftrightarrow & \color{red}{-8}x & = &17\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{17}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{8} } & & \\ & V = \left\{ \frac{-17}{8} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-3}& = &8 \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &-9x & = &11\\\Leftrightarrow & \color{red}{-9}x & = &11\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{11}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{9} } & & \\ & V = \left\{ \frac{-11}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-14}& = &8 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &8\color{blue}{+14} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{-13}& = &11 \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &3x & = &24\\\Leftrightarrow & \color{red}{3}x & = &24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{24}{3} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-3}& = &9 \\\Leftrightarrow & -8x \color{red}{-3}\color{blue}{+3} & = &9\color{blue}{+3} \\\Leftrightarrow &-8x & = &12\\\Leftrightarrow & \color{red}{-8}x & = &12\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{12}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{+12}& = &-5 \\\Leftrightarrow & 3x \color{red}{+12}\color{blue}{-12} & = &-5\color{blue}{-12} \\\Leftrightarrow &3x & = &-17\\\Leftrightarrow & \color{red}{3}x & = &-17\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-17}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+6}& = &-12 \\\Leftrightarrow & 12x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &12x & = &-18\\\Leftrightarrow & \color{red}{12}x & = &-18\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-18}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-5}& = &-13 \\\Leftrightarrow & 4x \color{red}{-5}\color{blue}{+5} & = &-13\color{blue}{+5} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+5}& = &-6 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &-x & = &-11\\\Leftrightarrow & \color{red}{-}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-11}{-1} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{+5}& = &-1 \\\Leftrightarrow & -x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+11}& = &-8 \\\Leftrightarrow & 13x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)