Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{-8}& = &-6 \\\Leftrightarrow & -13x \color{red}{-8}\color{blue}{+8} & = &-6\color{blue}{+8} \\\Leftrightarrow &-13x & = &2\\\Leftrightarrow & \color{red}{-13}x & = &2\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{2}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+4}& = &-14 \\\Leftrightarrow & 8x \color{red}{+4}\color{blue}{-4} & = &-14\color{blue}{-4} \\\Leftrightarrow &8x & = &-18\\\Leftrightarrow & \color{red}{8}x & = &-18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-7}& = &-3 \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7} & = &-3\color{blue}{+7} \\\Leftrightarrow &-9x & = &4\\\Leftrightarrow & \color{red}{-9}x & = &4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{9} } & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-9}& = &2 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &4x & = &11\\\Leftrightarrow & \color{red}{4}x & = &11\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{11}{4} \\\Leftrightarrow & \color{green}{ x = \frac{11}{4} } & & \\ & V = \left\{ \frac{11}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+6}& = &4 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &4\color{blue}{-6} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{+13}& = &-6 \\\Leftrightarrow & x \color{red}{+13}\color{blue}{-13} & = &-6\color{blue}{-13} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
7. \(\begin{align} & 3x \color{red}{-8}& = &-7 \\\Leftrightarrow & 3x \color{red}{-8}\color{blue}{+8} & = &-7\color{blue}{+8} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+11}& = &-14 \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11} & = &-14\color{blue}{-11} \\\Leftrightarrow &-14x & = &-25\\\Leftrightarrow & \color{red}{-14}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-25}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{25}{14} } & & \\ & V = \left\{ \frac{25}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & -2x \color{red}{-8}& = &-5 \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8} & = &-5\color{blue}{+8} \\\Leftrightarrow &-2x & = &3\\\Leftrightarrow & \color{red}{-2}x & = &3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-9}& = &-1 \\\Leftrightarrow & -7x \color{red}{-9}\color{blue}{+9} & = &-1\color{blue}{+9} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{-14}& = &10 \\\Leftrightarrow & -14x \color{red}{-14}\color{blue}{+14} & = &10\color{blue}{+14} \\\Leftrightarrow &-14x & = &24\\\Leftrightarrow & \color{red}{-14}x & = &24\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{24}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{7} } & & \\ & V = \left\{ \frac{-12}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+1}& = &3 \\\Leftrightarrow & -7x \color{red}{+1}\color{blue}{-1} & = &3\color{blue}{-1} \\\Leftrightarrow &-7x & = &2\\\Leftrightarrow & \color{red}{-7}x & = &2\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{2}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{7} } & & \\ & V = \left\{ \frac{-2}{7} \right\} & \\\end{align}\)