Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-2}& = &10 \\\Leftrightarrow & -6x \color{red}{-2}\color{blue}{+2} & = &10\color{blue}{+2} \\\Leftrightarrow &-6x & = &12\\\Leftrightarrow & \color{red}{-6}x & = &12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{12}{-6} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+8}& = &5 \\\Leftrightarrow & 10x \color{red}{+8}\color{blue}{-8} & = &5\color{blue}{-8} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{+2}& = &5 \\\Leftrightarrow & 8x \color{red}{+2}\color{blue}{-2} & = &5\color{blue}{-2} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{-5}& = &3 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &3\color{blue}{+5} \\\Leftrightarrow &8x & = &8\\\Leftrightarrow & \color{red}{8}x & = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-3}& = &-7 \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3} & = &-7\color{blue}{+3} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+13}& = &9 \\\Leftrightarrow & -13x \color{red}{+13}\color{blue}{-13} & = &9\color{blue}{-13} \\\Leftrightarrow &-13x & = &-4\\\Leftrightarrow & \color{red}{-13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-4}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{4}{13} } & & \\ & V = \left\{ \frac{4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-11}& = &-8 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{+2}& = &13 \\\Leftrightarrow & x \color{red}{+2}\color{blue}{-2} & = &13\color{blue}{-2} \\\Leftrightarrow &x & = &11\\\Leftrightarrow & \color{red}{}x & = &11\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 11 \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+14}& = &-5 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+14}& = &-15 \\\Leftrightarrow & -15x \color{red}{+14}\color{blue}{-14} & = &-15\color{blue}{-14} \\\Leftrightarrow &-15x & = &-29\\\Leftrightarrow & \color{red}{-15}x & = &-29\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-29}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{29}{15} } & & \\ & V = \left\{ \frac{29}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -14x \color{red}{+11}& = &-4 \\\Leftrightarrow & -14x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &-14x & = &-15\\\Leftrightarrow & \color{red}{-14}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-4}& = &9 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &9\color{blue}{+4} \\\Leftrightarrow &-3x & = &13\\\Leftrightarrow & \color{red}{-3}x & = &13\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{13}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)