Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{+2}& = &-13 \\\Leftrightarrow & -15x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &-15x & = &-15\\\Leftrightarrow & \color{red}{-15}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-15}{-15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 12x \color{red}{-2}& = &-12 \\\Leftrightarrow & 12x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &12x & = &-10\\\Leftrightarrow & \color{red}{12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-10}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & 11x \color{red}{+8}& = &-3 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &-3\color{blue}{-8} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{-9}& = &-12 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &-12\color{blue}{+9} \\\Leftrightarrow &7x & = &-3\\\Leftrightarrow & \color{red}{7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-4}& = &8 \\\Leftrightarrow & -4x \color{red}{-4}\color{blue}{+4} & = &8\color{blue}{+4} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+9}& = &-9 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-9\color{blue}{-9} \\\Leftrightarrow &x & = &-18\\\Leftrightarrow & \color{red}{}x & = &-18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -18 \\\Leftrightarrow & \color{green}{ x = -18 } & & \\ & V = \left\{ -18 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-7}& = &-13 \\\Leftrightarrow & 3x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &3x & = &-6\\\Leftrightarrow & \color{red}{3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-6}{3} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-3}& = &-1 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &-1\color{blue}{+3} \\\Leftrightarrow &-3x & = &2\\\Leftrightarrow & \color{red}{-3}x & = &2\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{2}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+14}& = &15 \\\Leftrightarrow & -9x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &-9x & = &1\\\Leftrightarrow & \color{red}{-9}x & = &1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{9} } & & \\ & V = \left\{ \frac{-1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & 6x \color{red}{-2}& = &-5 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-5\color{blue}{+2} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{+6}& = &-3 \\\Leftrightarrow & -15x \color{red}{+6}\color{blue}{-6} & = &-3\color{blue}{-6} \\\Leftrightarrow &-15x & = &-9\\\Leftrightarrow & \color{red}{-15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-9}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-15}& = &-2 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &7x & = &13\\\Leftrightarrow & \color{red}{7}x & = &13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{13}{7} } & & \\ & V = \left\{ \frac{13}{7} \right\} & \\\end{align}\)