Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 9x \color{red}{+4}& = &-10 \\\Leftrightarrow & 9x \color{red}{+4}\color{blue}{-4} & = &-10\color{blue}{-4} \\\Leftrightarrow &9x & = &-14\\\Leftrightarrow & \color{red}{9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-14}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{9} } & & \\ & V = \left\{ \frac{-14}{9} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{-12}& = &8 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &10x & = &20\\\Leftrightarrow & \color{red}{10}x & = &20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{20}{10} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-12}& = &-5 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &-5\color{blue}{+12} \\\Leftrightarrow &2x & = &7\\\Leftrightarrow & \color{red}{2}x & = &7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{+6}& = &-3 \\\Leftrightarrow & 2x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-14}& = &3 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &3\color{blue}{+14} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+7}& = &-12 \\\Leftrightarrow & -x \color{red}{+7}\color{blue}{-7} & = &-12\color{blue}{-7} \\\Leftrightarrow &-x & = &-19\\\Leftrightarrow & \color{red}{-}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-19}{-1} \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
7. \(\begin{align} & -8x \color{red}{-9}& = &-6 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-6\color{blue}{+9} \\\Leftrightarrow &-8x & = &3\\\Leftrightarrow & \color{red}{-8}x & = &3\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{3}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{8} } & & \\ & V = \left\{ \frac{-3}{8} \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{-3}& = &-9 \\\Leftrightarrow & 11x \color{red}{-3}\color{blue}{+3} & = &-9\color{blue}{+3} \\\Leftrightarrow &11x & = &-6\\\Leftrightarrow & \color{red}{11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-6}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{-8}& = &9 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &9\color{blue}{+8} \\\Leftrightarrow &14x & = &17\\\Leftrightarrow & \color{red}{14}x & = &17\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{17}{14} \\\Leftrightarrow & \color{green}{ x = \frac{17}{14} } & & \\ & V = \left\{ \frac{17}{14} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+4}& = &-12 \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4} & = &-12\color{blue}{-4} \\\Leftrightarrow &-x & = &-16\\\Leftrightarrow & \color{red}{-}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-16}{-1} \\\Leftrightarrow & \color{green}{ x = 16 } & & \\ & V = \left\{ 16 \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{+14}& = &-1 \\\Leftrightarrow & 4x \color{red}{+14}\color{blue}{-14} & = &-1\color{blue}{-14} \\\Leftrightarrow &4x & = &-15\\\Leftrightarrow & \color{red}{4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-15}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{4} } & & \\ & V = \left\{ \frac{-15}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{-8}& = &-15 \\\Leftrightarrow & -12x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)