Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+15}& = &8 \\\Leftrightarrow & 13x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{-4}& = &8 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &8\color{blue}{+4} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-5}& = &-3 \\\Leftrightarrow & 2x \color{red}{-5}\color{blue}{+5} & = &-3\color{blue}{+5} \\\Leftrightarrow &2x & = &2\\\Leftrightarrow & \color{red}{2}x & = &2\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{2}{2} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+10}& = &-15 \\\Leftrightarrow & 7x \color{red}{+10}\color{blue}{-10} & = &-15\color{blue}{-10} \\\Leftrightarrow &7x & = &-25\\\Leftrightarrow & \color{red}{7}x & = &-25\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-25}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{7} } & & \\ & V = \left\{ \frac{-25}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{-8}& = &-15 \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &-14x & = &-7\\\Leftrightarrow & \color{red}{-14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{+15}& = &8 \\\Leftrightarrow & -13x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &-13x & = &-7\\\Leftrightarrow & \color{red}{-13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-7}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-2}& = &7 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &7\color{blue}{+2} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-6}& = &7 \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &10x & = &13\\\Leftrightarrow & \color{red}{10}x & = &13\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{13}{10} \\\Leftrightarrow & \color{green}{ x = \frac{13}{10} } & & \\ & V = \left\{ \frac{13}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{+14}& = &1 \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14} & = &1\color{blue}{-14} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{-13}& = &-6 \\\Leftrightarrow & -12x \color{red}{-13}\color{blue}{+13} & = &-6\color{blue}{+13} \\\Leftrightarrow &-12x & = &7\\\Leftrightarrow & \color{red}{-12}x & = &7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{12} } & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-9}& = &13 \\\Leftrightarrow & -10x \color{red}{-9}\color{blue}{+9} & = &13\color{blue}{+9} \\\Leftrightarrow &-10x & = &22\\\Leftrightarrow & \color{red}{-10}x & = &22\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{22}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{-6}& = &-7 \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6} & = &-7\color{blue}{+6} \\\Leftrightarrow &10x & = &-1\\\Leftrightarrow & \color{red}{10}x & = &-1\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-1}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)