Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-12}& = &-1 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &-1\color{blue}{+12} \\\Leftrightarrow &6x & = &11\\\Leftrightarrow & \color{red}{6}x & = &11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+2}& = &13 \\\Leftrightarrow & 4x \color{red}{+2}\color{blue}{-2} & = &13\color{blue}{-2} \\\Leftrightarrow &4x & = &11\\\Leftrightarrow & \color{red}{4}x & = &11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -x \color{red}{+12}& = &-9 \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12} & = &-9\color{blue}{-12} \\\Leftrightarrow &-x & = &-21\\\Leftrightarrow & \color{red}{-}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-21}{-1} \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+3}& = &-3 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &-3\color{blue}{-3} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-12}& = &15 \\\Leftrightarrow & -4x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &-4x & = &27\\\Leftrightarrow & \color{red}{-4}x & = &27\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{27}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-27}{4} } & & \\ & V = \left\{ \frac{-27}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{-5}& = &-4 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &-4\color{blue}{+5} \\\Leftrightarrow &-2x & = &1\\\Leftrightarrow & \color{red}{-2}x & = &1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+11}& = &-7 \\\Leftrightarrow & 14x \color{red}{+11}\color{blue}{-11} & = &-7\color{blue}{-11} \\\Leftrightarrow &14x & = &-18\\\Leftrightarrow & \color{red}{14}x & = &-18\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-18}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-6}& = &-13 \\\Leftrightarrow & 3x \color{red}{-6}\color{blue}{+6} & = &-13\color{blue}{+6} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-4}& = &-1 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &-1\color{blue}{+4} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-2}& = &14 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &14\color{blue}{+2} \\\Leftrightarrow &8x & = &16\\\Leftrightarrow & \color{red}{8}x & = &16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{16}{8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & 11x \color{red}{-15}& = &-10 \\\Leftrightarrow & 11x \color{red}{-15}\color{blue}{+15} & = &-10\color{blue}{+15} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-6}& = &3 \\\Leftrightarrow & -14x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)