Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-2}& = &-11 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &-11\color{blue}{+2} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+2}& = &3 \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{+2}& = &12 \\\Leftrightarrow & -2x \color{red}{+2}\color{blue}{-2} & = &12\color{blue}{-2} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & -14x \color{red}{-2}& = &-14 \\\Leftrightarrow & -14x \color{red}{-2}\color{blue}{+2} & = &-14\color{blue}{+2} \\\Leftrightarrow &-14x & = &-12\\\Leftrightarrow & \color{red}{-14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{+7}& = &13 \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7} & = &13\color{blue}{-7} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+3}& = &2 \\\Leftrightarrow & -5x \color{red}{+3}\color{blue}{-3} & = &2\color{blue}{-3} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-1}& = &14 \\\Leftrightarrow & 14x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &14x & = &15\\\Leftrightarrow & \color{red}{14}x & = &15\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{15}{14} \\\Leftrightarrow & \color{green}{ x = \frac{15}{14} } & & \\ & V = \left\{ \frac{15}{14} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+11}& = &8 \\\Leftrightarrow & -11x \color{red}{+11}\color{blue}{-11} & = &8\color{blue}{-11} \\\Leftrightarrow &-11x & = &-3\\\Leftrightarrow & \color{red}{-11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{3}{11} } & & \\ & V = \left\{ \frac{3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 4x \color{red}{-12}& = &7 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &7\color{blue}{+12} \\\Leftrightarrow &4x & = &19\\\Leftrightarrow & \color{red}{4}x & = &19\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{19}{4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+7}& = &-12 \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7} & = &-12\color{blue}{-7} \\\Leftrightarrow &x & = &-19\\\Leftrightarrow & \color{red}{}x & = &-19\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -19 \\\Leftrightarrow & \color{green}{ x = -19 } & & \\ & V = \left\{ -19 \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-15}& = &8 \\\Leftrightarrow & -15x \color{red}{-15}\color{blue}{+15} & = &8\color{blue}{+15} \\\Leftrightarrow &-15x & = &23\\\Leftrightarrow & \color{red}{-15}x & = &23\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{23}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{-11}& = &7 \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &11x & = &18\\\Leftrightarrow & \color{red}{11}x & = &18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{18}{11} } & & \\ & V = \left\{ \frac{18}{11} \right\} & \\\end{align}\)