Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-15}& = &3 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &3\color{blue}{+15} \\\Leftrightarrow &6x & = &18\\\Leftrightarrow & \color{red}{6}x & = &18\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{18}{6} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+14}& = &4 \\\Leftrightarrow & -12x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+8}& = &-1 \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8} & = &-1\color{blue}{-8} \\\Leftrightarrow &4x & = &-9\\\Leftrightarrow & \color{red}{4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -2x \color{red}{+4}& = &-14 \\\Leftrightarrow & -2x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &-2x & = &-18\\\Leftrightarrow & \color{red}{-2}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-18}{-2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
5. \(\begin{align} & 12x \color{red}{+11}& = &-14 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &12x & = &-25\\\Leftrightarrow & \color{red}{12}x & = &-25\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-25}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{12} } & & \\ & V = \left\{ \frac{-25}{12} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{+12}& = &-11 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &-11\color{blue}{-12} \\\Leftrightarrow &4x & = &-23\\\Leftrightarrow & \color{red}{4}x & = &-23\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-23}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{4} } & & \\ & V = \left\{ \frac{-23}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -6x \color{red}{+9}& = &-3 \\\Leftrightarrow & -6x \color{red}{+9}\color{blue}{-9} & = &-3\color{blue}{-9} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{+1}& = &-5 \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1} & = &-5\color{blue}{-1} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -x \color{red}{+1}& = &-8 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-8\color{blue}{-1} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+6}& = &-3 \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &-7x & = &-9\\\Leftrightarrow & \color{red}{-7}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+5}& = &-7 \\\Leftrightarrow & -13x \color{red}{+5}\color{blue}{-5} & = &-7\color{blue}{-5} \\\Leftrightarrow &-13x & = &-12\\\Leftrightarrow & \color{red}{-13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-12}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{12}{13} } & & \\ & V = \left\{ \frac{12}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-5}& = &-5 \\\Leftrightarrow & 6x \color{red}{-5}\color{blue}{+5} & = &-5\color{blue}{+5} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)