Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+3}& = &-10 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &8x & = &-13\\\Leftrightarrow & \color{red}{8}x & = &-13\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-13}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & 3x \color{red}{+13}& = &11 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &11\color{blue}{-13} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+15}& = &-5 \\\Leftrightarrow & 11x \color{red}{+15}\color{blue}{-15} & = &-5\color{blue}{-15} \\\Leftrightarrow &11x & = &-20\\\Leftrightarrow & \color{red}{11}x & = &-20\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-20}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{-5}& = &-12 \\\Leftrightarrow & -4x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-4x & = &-7\\\Leftrightarrow & \color{red}{-4}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{4} } & & \\ & V = \left\{ \frac{7}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -x \color{red}{+4}& = &3 \\\Leftrightarrow & -x \color{red}{+4}\color{blue}{-4} & = &3\color{blue}{-4} \\\Leftrightarrow &-x & = &-1\\\Leftrightarrow & \color{red}{-}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-1}{-1} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-4}& = &-15 \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4} & = &-15\color{blue}{+4} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+4}& = &-11 \\\Leftrightarrow & 10x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &10x & = &-15\\\Leftrightarrow & \color{red}{10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-15}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+3}& = &-13 \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &-10x & = &-16\\\Leftrightarrow & \color{red}{-10}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-16}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -5x \color{red}{-11}& = &-6 \\\Leftrightarrow & -5x \color{red}{-11}\color{blue}{+11} & = &-6\color{blue}{+11} \\\Leftrightarrow &-5x & = &5\\\Leftrightarrow & \color{red}{-5}x & = &5\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{5}{-5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
10. \(\begin{align} & 15x \color{red}{+6}& = &-8 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &-8\color{blue}{-6} \\\Leftrightarrow &15x & = &-14\\\Leftrightarrow & \color{red}{15}x & = &-14\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-14}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{15} } & & \\ & V = \left\{ \frac{-14}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-8}& = &2 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &2\color{blue}{+8} \\\Leftrightarrow &-3x & = &10\\\Leftrightarrow & \color{red}{-3}x & = &10\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{10}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{3} } & & \\ & V = \left\{ \frac{-10}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{+6}& = &15 \\\Leftrightarrow & -14x \color{red}{+6}\color{blue}{-6} & = &15\color{blue}{-6} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)