Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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