Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+4}& = &-12 \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4} & = &-12\color{blue}{-4} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-12}& = &5 \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &15x & = &17\\\Leftrightarrow & \color{red}{15}x & = &17\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{17}{15} \\\Leftrightarrow & \color{green}{ x = \frac{17}{15} } & & \\ & V = \left\{ \frac{17}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{-15}& = &1 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &1\color{blue}{+15} \\\Leftrightarrow &6x & = &16\\\Leftrightarrow & \color{red}{6}x & = &16\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{16}{6} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-8}& = &-11 \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &-14x & = &-3\\\Leftrightarrow & \color{red}{-14}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{3}{14} } & & \\ & V = \left\{ \frac{3}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-4}& = &9 \\\Leftrightarrow & 6x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &6x & = &13\\\Leftrightarrow & \color{red}{6}x & = &13\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{13}{6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = &-14 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &-14\color{blue}{+15} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-2}& = &-3 \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2} & = &-3\color{blue}{+2} \\\Leftrightarrow &2x & = &-1\\\Leftrightarrow & \color{red}{2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-1}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -6x \color{red}{+10}& = &7 \\\Leftrightarrow & -6x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-8}& = &-7 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &-7\color{blue}{+8} \\\Leftrightarrow &-4x & = &1\\\Leftrightarrow & \color{red}{-4}x & = &1\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{1}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = &-5 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-5\color{blue}{-1} \\\Leftrightarrow &-x & = &-6\\\Leftrightarrow & \color{red}{-}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-6}{-1} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+2}& = &-11 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-11\color{blue}{-2} \\\Leftrightarrow &10x & = &-13\\\Leftrightarrow & \color{red}{10}x & = &-13\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-13}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{10} } & & \\ & V = \left\{ \frac{-13}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -x \color{red}{-4}& = &-8 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &-8\color{blue}{+4} \\\Leftrightarrow &-x & = &-4\\\Leftrightarrow & \color{red}{-}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-4}{-1} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)