Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{-8}& = &-2 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &-2\color{blue}{+8} \\\Leftrightarrow &-11x & = &6\\\Leftrightarrow & \color{red}{-11}x & = &6\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{6}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{11} } & & \\ & V = \left\{ \frac{-6}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+13}& = &-15 \\\Leftrightarrow & -2x \color{red}{+13}\color{blue}{-13} & = &-15\color{blue}{-13} \\\Leftrightarrow &-2x & = &-28\\\Leftrightarrow & \color{red}{-2}x & = &-28\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-28}{-2} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
3. \(\begin{align} & 14x \color{red}{-11}& = &-10 \\\Leftrightarrow & 14x \color{red}{-11}\color{blue}{+11} & = &-10\color{blue}{+11} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+13}& = &8 \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13} & = &8\color{blue}{-13} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{-13}& = &7 \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13} & = &7\color{blue}{+13} \\\Leftrightarrow &x & = &20\\\Leftrightarrow & \color{red}{}x & = &20\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 20 \\\Leftrightarrow & \color{green}{ x = 20 } & & \\ & V = \left\{ 20 \right\} & \\\end{align}\)
6. \(\begin{align} & -5x \color{red}{+1}& = &15 \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1} & = &15\color{blue}{-1} \\\Leftrightarrow &-5x & = &14\\\Leftrightarrow & \color{red}{-5}x & = &14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-14}{5} } & & \\ & V = \left\{ \frac{-14}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-3}& = &-10 \\\Leftrightarrow & 2x \color{red}{-3}\color{blue}{+3} & = &-10\color{blue}{+3} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{+2}& = &3 \\\Leftrightarrow & 9x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-11}& = &-10 \\\Leftrightarrow & 15x \color{red}{-11}\color{blue}{+11} & = &-10\color{blue}{+11} \\\Leftrightarrow &15x & = &1\\\Leftrightarrow & \color{red}{15}x & = &1\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{1}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+15}& = &-1 \\\Leftrightarrow & 4x \color{red}{+15}\color{blue}{-15} & = &-1\color{blue}{-15} \\\Leftrightarrow &4x & = &-16\\\Leftrightarrow & \color{red}{4}x & = &-16\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-16}{4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{-8}& = &4 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &4\color{blue}{+8} \\\Leftrightarrow &15x & = &12\\\Leftrightarrow & \color{red}{15}x & = &12\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{12}{15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-3}& = &14 \\\Leftrightarrow & x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)