Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{+3}& = &-12 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &-12\color{blue}{-3} \\\Leftrightarrow &10x & = &-15\\\Leftrightarrow & \color{red}{10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+4}& = &-6 \\\Leftrightarrow & -6x \color{red}{+4}\color{blue}{-4} & = &-6\color{blue}{-4} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+8}& = &8 \\\Leftrightarrow & x \color{red}{+8}\color{blue}{-8} & = &8\color{blue}{-8} \\\Leftrightarrow &x & = &0\\\Leftrightarrow & \color{red}{}x & = &0\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 0 \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-1}& = &-2 \\\Leftrightarrow & 15x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &15x & = &-1\\\Leftrightarrow & \color{red}{15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-4}& = &10 \\\Leftrightarrow & -14x \color{red}{-4}\color{blue}{+4} & = &10\color{blue}{+4} \\\Leftrightarrow &-14x & = &14\\\Leftrightarrow & \color{red}{-14}x & = &14\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{14}{-14} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-1}& = &-9 \\\Leftrightarrow & -15x \color{red}{-1}\color{blue}{+1} & = &-9\color{blue}{+1} \\\Leftrightarrow &-15x & = &-8\\\Leftrightarrow & \color{red}{-15}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{8}{15} } & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 11x \color{red}{+9}& = &-2 \\\Leftrightarrow & 11x \color{red}{+9}\color{blue}{-9} & = &-2\color{blue}{-9} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
8. \(\begin{align} & 11x \color{red}{+13}& = &12 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-7}& = &10 \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7} & = &10\color{blue}{+7} \\\Leftrightarrow &-12x & = &17\\\Leftrightarrow & \color{red}{-12}x & = &17\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{17}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{12} } & & \\ & V = \left\{ \frac{-17}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+12}& = &-15 \\\Leftrightarrow & -x \color{red}{+12}\color{blue}{-12} & = &-15\color{blue}{-12} \\\Leftrightarrow &-x & = &-27\\\Leftrightarrow & \color{red}{-}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-27}{-1} \\\Leftrightarrow & \color{green}{ x = 27 } & & \\ & V = \left\{ 27 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{-8}& = &11 \\\Leftrightarrow & x \color{red}{-8}\color{blue}{+8} & = &11\color{blue}{+8} \\\Leftrightarrow &x & = &19\\\Leftrightarrow & \color{red}{}x & = &19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 19 \\\Leftrightarrow & \color{green}{ x = 19 } & & \\ & V = \left\{ 19 \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{-12}& = &-9 \\\Leftrightarrow & 6x \color{red}{-12}\color{blue}{+12} & = &-9\color{blue}{+12} \\\Leftrightarrow &6x & = &3\\\Leftrightarrow & \color{red}{6}x & = &3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)