Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+13}& = &-12 \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &-6x & = &-25\\\Leftrightarrow & \color{red}{-6}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-25}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{25}{6} } & & \\ & V = \left\{ \frac{25}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-1}& = &14 \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1} & = &14\color{blue}{+1} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-1}& = &-8 \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1} & = &-8\color{blue}{+1} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{-15}& = &-3 \\\Leftrightarrow & 4x \color{red}{-15}\color{blue}{+15} & = &-3\color{blue}{+15} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-2}& = &-5 \\\Leftrightarrow & 5x \color{red}{-2}\color{blue}{+2} & = &-5\color{blue}{+2} \\\Leftrightarrow &5x & = &-3\\\Leftrightarrow & \color{red}{5}x & = &-3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{-4}& = &-15 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &-15\color{blue}{+4} \\\Leftrightarrow &15x & = &-11\\\Leftrightarrow & \color{red}{15}x & = &-11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{15} } & & \\ & V = \left\{ \frac{-11}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{-14}& = &-13 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &-13\color{blue}{+14} \\\Leftrightarrow &-2x & = &1\\\Leftrightarrow & \color{red}{-2}x & = &1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{+10}& = &-10 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{-9}& = &-2 \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9} & = &-2\color{blue}{+9} \\\Leftrightarrow &x & = &7\\\Leftrightarrow & \color{red}{}x & = &7\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 7 \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-14}& = &-11 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14} & = &-11\color{blue}{+14} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-10}& = &10 \\\Leftrightarrow & -x \color{red}{-10}\color{blue}{+10} & = &10\color{blue}{+10} \\\Leftrightarrow &-x & = &20\\\Leftrightarrow & \color{red}{-}x & = &20\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{20}{-1} \\\Leftrightarrow & \color{green}{ x = -20 } & & \\ & V = \left\{ -20 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+5}& = &14 \\\Leftrightarrow & 9x \color{red}{+5}\color{blue}{-5} & = &14\color{blue}{-5} \\\Leftrightarrow &9x & = &9\\\Leftrightarrow & \color{red}{9}x & = &9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{9}{9} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)