Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-13}& = &11 \\\Leftrightarrow & -13x \color{red}{-13}\color{blue}{+13} & = &11\color{blue}{+13} \\\Leftrightarrow &-13x & = &24\\\Leftrightarrow & \color{red}{-13}x & = &24\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{24}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-2}& = &8 \\\Leftrightarrow & -8x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &-8x & = &10\\\Leftrightarrow & \color{red}{-8}x & = &10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-7}& = &-10 \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7} & = &-10\color{blue}{+7} \\\Leftrightarrow &-5x & = &-3\\\Leftrightarrow & \color{red}{-5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-10}& = &11 \\\Leftrightarrow & 6x \color{red}{-10}\color{blue}{+10} & = &11\color{blue}{+10} \\\Leftrightarrow &6x & = &21\\\Leftrightarrow & \color{red}{6}x & = &21\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{21}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+7}& = &-6 \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &13x & = &-13\\\Leftrightarrow & \color{red}{13}x & = &-13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-13}{13} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+12}& = &14 \\\Leftrightarrow & -14x \color{red}{+12}\color{blue}{-12} & = &14\color{blue}{-12} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+4}& = &12 \\\Leftrightarrow & -5x \color{red}{+4}\color{blue}{-4} & = &12\color{blue}{-4} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+10}& = &-4 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &-4\color{blue}{-10} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+11}& = &-13 \\\Leftrightarrow & 3x \color{red}{+11}\color{blue}{-11} & = &-13\color{blue}{-11} \\\Leftrightarrow &3x & = &-24\\\Leftrightarrow & \color{red}{3}x & = &-24\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-24}{3} \\\Leftrightarrow & \color{green}{ x = -8 } & & \\ & V = \left\{ -8 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{+14}& = &-8 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &-8\color{blue}{-14} \\\Leftrightarrow &-3x & = &-22\\\Leftrightarrow & \color{red}{-3}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-22}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{22}{3} } & & \\ & V = \left\{ \frac{22}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+15}& = &7 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &7\color{blue}{-15} \\\Leftrightarrow &13x & = &-8\\\Leftrightarrow & \color{red}{13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{13} } & & \\ & V = \left\{ \frac{-8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -8x \color{red}{+11}& = &-3 \\\Leftrightarrow & -8x \color{red}{+11}\color{blue}{-11} & = &-3\color{blue}{-11} \\\Leftrightarrow &-8x & = &-14\\\Leftrightarrow & \color{red}{-8}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-14}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)