Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+9}& = &-12 \\\Leftrightarrow & 14x \color{red}{+9}\color{blue}{-9} & = &-12\color{blue}{-9} \\\Leftrightarrow &14x & = &-21\\\Leftrightarrow & \color{red}{14}x & = &-21\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-21}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+5}& = &-1 \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &-11x & = &-6\\\Leftrightarrow & \color{red}{-11}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{6}{11} } & & \\ & V = \left\{ \frac{6}{11} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+7}& = &3 \\\Leftrightarrow & -5x \color{red}{+7}\color{blue}{-7} & = &3\color{blue}{-7} \\\Leftrightarrow &-5x & = &-4\\\Leftrightarrow & \color{red}{-5}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-4}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+12}& = &-12 \\\Leftrightarrow & 11x \color{red}{+12}\color{blue}{-12} & = &-12\color{blue}{-12} \\\Leftrightarrow &11x & = &-24\\\Leftrightarrow & \color{red}{11}x & = &-24\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-24}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-24}{11} } & & \\ & V = \left\{ \frac{-24}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -12x \color{red}{-9}& = &-9 \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9} & = &-9\color{blue}{+9} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+14}& = &5 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+11}& = &-15 \\\Leftrightarrow & -x \color{red}{+11}\color{blue}{-11} & = &-15\color{blue}{-11} \\\Leftrightarrow &-x & = &-26\\\Leftrightarrow & \color{red}{-}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-26}{-1} \\\Leftrightarrow & \color{green}{ x = 26 } & & \\ & V = \left\{ 26 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+3}& = &15 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &11x & = &12\\\Leftrightarrow & \color{red}{11}x & = &12\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{12}{11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-13}& = &-5 \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13} & = &-5\color{blue}{+13} \\\Leftrightarrow &15x & = &8\\\Leftrightarrow & \color{red}{15}x & = &8\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{8}{15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -10x \color{red}{-1}& = &-10 \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1} & = &-10\color{blue}{+1} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-3}& = &12 \\\Leftrightarrow & -x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &-x & = &15\\\Leftrightarrow & \color{red}{-}x & = &15\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{15}{-1} \\\Leftrightarrow & \color{green}{ x = -15 } & & \\ & V = \left\{ -15 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-7}& = &-2 \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &x & = &5\\\Leftrightarrow & \color{red}{}x & = &5\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 5 \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)