Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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