Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+5}& = &-14 \\\Leftrightarrow & 13x \color{red}{+5}\color{blue}{-5} & = &-14\color{blue}{-5} \\\Leftrightarrow &13x & = &-19\\\Leftrightarrow & \color{red}{13}x & = &-19\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-19}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{13} } & & \\ & V = \left\{ \frac{-19}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-8}& = &14 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &14\color{blue}{+8} \\\Leftrightarrow &-4x & = &22\\\Leftrightarrow & \color{red}{-4}x & = &22\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{22}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{2} } & & \\ & V = \left\{ \frac{-11}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{+7}& = &7 \\\Leftrightarrow & -13x \color{red}{+7}\color{blue}{-7} & = &7\color{blue}{-7} \\\Leftrightarrow &-13x & = &0\\\Leftrightarrow & \color{red}{-13}x & = &0\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{0}{-13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+1}& = &-1 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & -7x \color{red}{-5}& = &-12 \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-13}& = &13 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &13\color{blue}{+13} \\\Leftrightarrow &8x & = &26\\\Leftrightarrow & \color{red}{8}x & = &26\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{26}{8} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+1}& = &9 \\\Leftrightarrow & -14x \color{red}{+1}\color{blue}{-1} & = &9\color{blue}{-1} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+3}& = &-8 \\\Leftrightarrow & 10x \color{red}{+3}\color{blue}{-3} & = &-8\color{blue}{-3} \\\Leftrightarrow &10x & = &-11\\\Leftrightarrow & \color{red}{10}x & = &-11\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-11}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{-9}& = &-8 \\\Leftrightarrow & -15x \color{red}{-9}\color{blue}{+9} & = &-8\color{blue}{+9} \\\Leftrightarrow &-15x & = &1\\\Leftrightarrow & \color{red}{-15}x & = &1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{15} } & & \\ & V = \left\{ \frac{-1}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{-7}& = &-13 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &-13\color{blue}{+7} \\\Leftrightarrow &-6x & = &-6\\\Leftrightarrow & \color{red}{-6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-6}{-6} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-9}& = &2 \\\Leftrightarrow & 7x \color{red}{-9}\color{blue}{+9} & = &2\color{blue}{+9} \\\Leftrightarrow &7x & = &11\\\Leftrightarrow & \color{red}{7}x & = &11\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{11}{7} \\\Leftrightarrow & \color{green}{ x = \frac{11}{7} } & & \\ & V = \left\{ \frac{11}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+8}& = &13 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &13\color{blue}{-8} \\\Leftrightarrow &-12x & = &5\\\Leftrightarrow & \color{red}{-12}x & = &5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{12} } & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)