Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+10}& = &-14 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &-14\color{blue}{-10} \\\Leftrightarrow &13x & = &-24\\\Leftrightarrow & \color{red}{13}x & = &-24\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-24}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{13} } & & \\ & V = \left\{ \frac{-24}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-12}& = &9 \\\Leftrightarrow & -9x \color{red}{-12}\color{blue}{+12} & = &9\color{blue}{+12} \\\Leftrightarrow &-9x & = &21\\\Leftrightarrow & \color{red}{-9}x & = &21\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{21}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-8}& = &-9 \\\Leftrightarrow & -5x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -x \color{red}{+6}& = &-15 \\\Leftrightarrow & -x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &-x & = &-21\\\Leftrightarrow & \color{red}{-}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-21}{-1} \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+9}& = &4 \\\Leftrightarrow & -11x \color{red}{+9}\color{blue}{-9} & = &4\color{blue}{-9} \\\Leftrightarrow &-11x & = &-5\\\Leftrightarrow & \color{red}{-11}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-5}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+14}& = &2 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+15}& = &-7 \\\Leftrightarrow & 6x \color{red}{+15}\color{blue}{-15} & = &-7\color{blue}{-15} \\\Leftrightarrow &6x & = &-22\\\Leftrightarrow & \color{red}{6}x & = &-22\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-22}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
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. \(\begin{align} & -6x \color{red}{-14}& = &3 \\\Leftrightarrow & -6x \color{red}{-14}\color{blue}{+14} & = &3\color{blue}{+14} \\\Leftrightarrow &-6x & = &17\\\Leftrightarrow & \color{red}{-6}x & = &17\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{17}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{6} } & & \\ & V = \left\{ \frac{-17}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-10}& = &-5 \\\Leftrightarrow & 13x \color{red}{-10}\color{blue}{+10} & = &-5\color{blue}{+10} \\\Leftrightarrow &13x & = &5\\\Leftrightarrow & \color{red}{13}x & = &5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+12}& = &2 \\\Leftrightarrow & -13x \color{red}{+12}\color{blue}{-12} & = &2\color{blue}{-12} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+3}& = &-13 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &7x & = &-16\\\Leftrightarrow & \color{red}{7}x & = &-16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{7} } & & \\ & V = \left\{ \frac{-16}{7} \right\} & \\\end{align}\)