Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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