Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{+5}& = &12 \\\Leftrightarrow & 11x \color{red}{+5}\color{blue}{-5} & = &12\color{blue}{-5} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{+3}& = &9 \\\Leftrightarrow & 6x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &6x & = &6\\\Leftrightarrow & \color{red}{6}x & = &6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{6}{6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{-9}& = &5 \\\Leftrightarrow & 4x \color{red}{-9}\color{blue}{+9} & = &5\color{blue}{+9} \\\Leftrightarrow &4x & = &14\\\Leftrightarrow & \color{red}{4}x & = &14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 10x \color{red}{+15}& = &3 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &3\color{blue}{-15} \\\Leftrightarrow &10x & = &-12\\\Leftrightarrow & \color{red}{10}x & = &-12\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-12}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{5} } & & \\ & V = \left\{ \frac{-6}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 15x \color{red}{+6}& = &3 \\\Leftrightarrow & 15x \color{red}{+6}\color{blue}{-6} & = &3\color{blue}{-6} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-11}& = &-3 \\\Leftrightarrow & -10x \color{red}{-11}\color{blue}{+11} & = &-3\color{blue}{+11} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-3}& = &-7 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &-7\color{blue}{+3} \\\Leftrightarrow &7x & = &-4\\\Leftrightarrow & \color{red}{7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-4}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-2}& = &-2 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &-2\color{blue}{+2} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+15}& = &-9 \\\Leftrightarrow & -4x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &-4x & = &-24\\\Leftrightarrow & \color{red}{-4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-24}{-4} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
10. \(\begin{align} & -3x \color{red}{-6}& = &-3 \\\Leftrightarrow & -3x \color{red}{-6}\color{blue}{+6} & = &-3\color{blue}{+6} \\\Leftrightarrow &-3x & = &3\\\Leftrightarrow & \color{red}{-3}x & = &3\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{3}{-3} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & x \color{red}{+9}& = &-3 \\\Leftrightarrow & x \color{red}{+9}\color{blue}{-9} & = &-3\color{blue}{-9} \\\Leftrightarrow &x & = &-12\\\Leftrightarrow & \color{red}{}x & = &-12\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -12 \\\Leftrightarrow & \color{green}{ x = -12 } & & \\ & V = \left\{ -12 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{+13}& = &-3 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &-3\color{blue}{-13} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)