Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -10x \color{red}{+14}& = &-10 \\\Leftrightarrow & -10x \color{red}{+14}\color{blue}{-14} & = &-10\color{blue}{-14} \\\Leftrightarrow &-10x & = &-24\\\Leftrightarrow & \color{red}{-10}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-24}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+1}& = &-9 \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 15x \color{red}{+7}& = &-9 \\\Leftrightarrow & 15x \color{red}{+7}\color{blue}{-7} & = &-9\color{blue}{-7} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
4. \(\begin{align} & 6x \color{red}{-13}& = &10 \\\Leftrightarrow & 6x \color{red}{-13}\color{blue}{+13} & = &10\color{blue}{+13} \\\Leftrightarrow &6x & = &23\\\Leftrightarrow & \color{red}{6}x & = &23\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{23}{6} \\\Leftrightarrow & \color{green}{ x = \frac{23}{6} } & & \\ & V = \left\{ \frac{23}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+7}& = &6 \\\Leftrightarrow & 13x \color{red}{+7}\color{blue}{-7} & = &6\color{blue}{-7} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-7}& = &-14 \\\Leftrightarrow & 6x \color{red}{-7}\color{blue}{+7} & = &-14\color{blue}{+7} \\\Leftrightarrow &6x & = &-7\\\Leftrightarrow & \color{red}{6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{-12}& = &5 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &12x & = &17\\\Leftrightarrow & \color{red}{12}x & = &17\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{17}{12} \\\Leftrightarrow & \color{green}{ x = \frac{17}{12} } & & \\ & V = \left\{ \frac{17}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{+4}& = &9 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &9\color{blue}{-4} \\\Leftrightarrow &-15x & = &5\\\Leftrightarrow & \color{red}{-15}x & = &5\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{5}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & x \color{red}{+3}& = &-3 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &-3\color{blue}{-3} \\\Leftrightarrow &x & = &-6\\\Leftrightarrow & \color{red}{}x & = &-6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -6 \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
10. \(\begin{align} & 11x \color{red}{+7}& = &-9 \\\Leftrightarrow & 11x \color{red}{+7}\color{blue}{-7} & = &-9\color{blue}{-7} \\\Leftrightarrow &11x & = &-16\\\Leftrightarrow & \color{red}{11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-16}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+12}& = &7 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &8x & = &-5\\\Leftrightarrow & \color{red}{8}x & = &-5\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-5}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{8} } & & \\ & V = \left\{ \frac{-5}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+10}& = &-10 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &-10\color{blue}{-10} \\\Leftrightarrow &14x & = &-20\\\Leftrightarrow & \color{red}{14}x & = &-20\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-20}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)