Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{-4}& = &-3 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-3\color{blue}{+4} \\\Leftrightarrow &13x & = &1\\\Leftrightarrow & \color{red}{13}x & = &1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+7}& = &7 \\\Leftrightarrow & -15x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-10}& = &5 \\\Leftrightarrow & -14x \color{red}{-10}\color{blue}{+10} & = &5\color{blue}{+10} \\\Leftrightarrow &-14x & = &15\\\Leftrightarrow & \color{red}{-14}x & = &15\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{15}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{14} } & & \\ & V = \left\{ \frac{-15}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -6x \color{red}{+13}& = &-2 \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13} & = &-2\color{blue}{-13} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+3}& = &14 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &14\color{blue}{-3} \\\Leftrightarrow &9x & = &11\\\Leftrightarrow & \color{red}{9}x & = &11\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{11}{9} \\\Leftrightarrow & \color{green}{ x = \frac{11}{9} } & & \\ & V = \left\{ \frac{11}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-5}& = &3 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &3\color{blue}{+5} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & 12x \color{red}{+1}& = &-3 \\\Leftrightarrow & 12x \color{red}{+1}\color{blue}{-1} & = &-3\color{blue}{-1} \\\Leftrightarrow &12x & = &-4\\\Leftrightarrow & \color{red}{12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -5x \color{red}{-15}& = &4 \\\Leftrightarrow & -5x \color{red}{-15}\color{blue}{+15} & = &4\color{blue}{+15} \\\Leftrightarrow &-5x & = &19\\\Leftrightarrow & \color{red}{-5}x & = &19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{5} } & & \\ & V = \left\{ \frac{-19}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{+7}& = &-3 \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7} & = &-3\color{blue}{-7} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & 10x \color{red}{-7}& = &9 \\\Leftrightarrow & 10x \color{red}{-7}\color{blue}{+7} & = &9\color{blue}{+7} \\\Leftrightarrow &10x & = &16\\\Leftrightarrow & \color{red}{10}x & = &16\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{16}{10} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 15x \color{red}{+2}& = &8 \\\Leftrightarrow & 15x \color{red}{+2}\color{blue}{-2} & = &8\color{blue}{-2} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{+10}& = &-13 \\\Leftrightarrow & 15x \color{red}{+10}\color{blue}{-10} & = &-13\color{blue}{-10} \\\Leftrightarrow &15x & = &-23\\\Leftrightarrow & \color{red}{15}x & = &-23\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-23}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{15} } & & \\ & V = \left\{ \frac{-23}{15} \right\} & \\\end{align}\)