Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+9}& = &11 \\\Leftrightarrow & -5x \color{red}{+9}\color{blue}{-9} & = &11\color{blue}{-9} \\\Leftrightarrow &-5x & = &2\\\Leftrightarrow & \color{red}{-5}x & = &2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+15}& = &5 \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15} & = &5\color{blue}{-15} \\\Leftrightarrow &4x & = &-10\\\Leftrightarrow & \color{red}{4}x & = &-10\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-10}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-9}& = &-10 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &-10\color{blue}{+9} \\\Leftrightarrow &-14x & = &-1\\\Leftrightarrow & \color{red}{-14}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-1}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+8}& = &-10 \\\Leftrightarrow & -4x \color{red}{+8}\color{blue}{-8} & = &-10\color{blue}{-8} \\\Leftrightarrow &-4x & = &-18\\\Leftrightarrow & \color{red}{-4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+14}& = &13 \\\Leftrightarrow & -13x \color{red}{+14}\color{blue}{-14} & = &13\color{blue}{-14} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-15}& = &4 \\\Leftrightarrow & 7x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &7x & = &19\\\Leftrightarrow & \color{red}{7}x & = &19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{19}{7} } & & \\ & V = \left\{ \frac{19}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-3}& = &11 \\\Leftrightarrow & 14x \color{red}{-3}\color{blue}{+3} & = &11\color{blue}{+3} \\\Leftrightarrow &14x & = &14\\\Leftrightarrow & \color{red}{14}x & = &14\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{14}{14} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-5}& = &-5 \\\Leftrightarrow & -2x \color{red}{-5}\color{blue}{+5} & = &-5\color{blue}{+5} \\\Leftrightarrow &-2x & = &0\\\Leftrightarrow & \color{red}{-2}x & = &0\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{0}{-2} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -10x \color{red}{-2}& = &13 \\\Leftrightarrow & -10x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &-10x & = &15\\\Leftrightarrow & \color{red}{-10}x & = &15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-4}& = &12 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &13x & = &16\\\Leftrightarrow & \color{red}{13}x & = &16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{16}{13} } & & \\ & V = \left\{ \frac{16}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-6}& = &-8 \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6} & = &-8\color{blue}{+6} \\\Leftrightarrow &13x & = &-2\\\Leftrightarrow & \color{red}{13}x & = &-2\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-2}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{13} } & & \\ & V = \left\{ \frac{-2}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{-5}& = &7 \\\Leftrightarrow & 7x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &7x & = &12\\\Leftrightarrow & \color{red}{7}x & = &12\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{12}{7} \\\Leftrightarrow & \color{green}{ x = \frac{12}{7} } & & \\ & V = \left\{ \frac{12}{7} \right\} & \\\end{align}\)