Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{+15}& = &10 \\\Leftrightarrow & 14x \color{red}{+15}\color{blue}{-15} & = &10\color{blue}{-15} \\\Leftrightarrow &14x & = &-5\\\Leftrightarrow & \color{red}{14}x & = &-5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{14} } & & \\ & V = \left\{ \frac{-5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & -6x \color{red}{+2}& = &15 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &15\color{blue}{-2} \\\Leftrightarrow &-6x & = &13\\\Leftrightarrow & \color{red}{-6}x & = &13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+13}& = &-11 \\\Leftrightarrow & -9x \color{red}{+13}\color{blue}{-13} & = &-11\color{blue}{-13} \\\Leftrightarrow &-9x & = &-24\\\Leftrightarrow & \color{red}{-9}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-24}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{3} } & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{-6}& = &15 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &15\color{blue}{+6} \\\Leftrightarrow &-6x & = &21\\\Leftrightarrow & \color{red}{-6}x & = &21\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{21}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-15}& = &-15 \\\Leftrightarrow & 10x \color{red}{-15}\color{blue}{+15} & = &-15\color{blue}{+15} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{+2}& = &-10 \\\Leftrightarrow & 3x \color{red}{+2}\color{blue}{-2} & = &-10\color{blue}{-2} \\\Leftrightarrow &3x & = &-12\\\Leftrightarrow & \color{red}{3}x & = &-12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-12}{3} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+5}& = &14 \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5} & = &14\color{blue}{-5} \\\Leftrightarrow &-12x & = &9\\\Leftrightarrow & \color{red}{-12}x & = &9\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{9}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-12}& = &4 \\\Leftrightarrow & -15x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &-15x & = &16\\\Leftrightarrow & \color{red}{-15}x & = &16\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{16}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{+7}& = &6 \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7} & = &6\color{blue}{-7} \\\Leftrightarrow &11x & = &-1\\\Leftrightarrow & \color{red}{11}x & = &-1\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-1}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-9}& = &14 \\\Leftrightarrow & -12x \color{red}{-9}\color{blue}{+9} & = &14\color{blue}{+9} \\\Leftrightarrow &-12x & = &23\\\Leftrightarrow & \color{red}{-12}x & = &23\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{23}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{12} } & & \\ & V = \left\{ \frac{-23}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-5}& = &10 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &10\color{blue}{+5} \\\Leftrightarrow &8x & = &15\\\Leftrightarrow & \color{red}{8}x & = &15\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{15}{8} \\\Leftrightarrow & \color{green}{ x = \frac{15}{8} } & & \\ & V = \left\{ \frac{15}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 13x \color{red}{+10}& = &6 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &6\color{blue}{-10} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)