Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-13}& = &-6 \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13} & = &-6\color{blue}{+13} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{+1}& = &-1 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-1\color{blue}{-1} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{+11}& = &5 \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &2x & = &-6\\\Leftrightarrow & \color{red}{2}x & = &-6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-6}{2} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+4}& = &13 \\\Leftrightarrow & -7x \color{red}{+4}\color{blue}{-4} & = &13\color{blue}{-4} \\\Leftrightarrow &-7x & = &9\\\Leftrightarrow & \color{red}{-7}x & = &9\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{9}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{7} } & & \\ & V = \left\{ \frac{-9}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -13x \color{red}{+3}& = &-12 \\\Leftrightarrow & -13x \color{red}{+3}\color{blue}{-3} & = &-12\color{blue}{-3} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-3}& = &-8 \\\Leftrightarrow & -12x \color{red}{-3}\color{blue}{+3} & = &-8\color{blue}{+3} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+13}& = &-13 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &-13\color{blue}{-13} \\\Leftrightarrow &9x & = &-26\\\Leftrightarrow & \color{red}{9}x & = &-26\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-26}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{9} } & & \\ & V = \left\{ \frac{-26}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+6}& = &3 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &3\color{blue}{-6} \\\Leftrightarrow &13x & = &-3\\\Leftrightarrow & \color{red}{13}x & = &-3\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-3}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-3}& = &14 \\\Leftrightarrow & 8x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{+7}& = &-5 \\\Leftrightarrow & -4x \color{red}{+7}\color{blue}{-7} & = &-5\color{blue}{-7} \\\Leftrightarrow &-4x & = &-12\\\Leftrightarrow & \color{red}{-4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-12}{-4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{-2}& = &5 \\\Leftrightarrow & 8x \color{red}{-2}\color{blue}{+2} & = &5\color{blue}{+2} \\\Leftrightarrow &8x & = &7\\\Leftrightarrow & \color{red}{8}x & = &7\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{7}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{8} } & & \\ & V = \left\{ \frac{7}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & -15x \color{red}{-5}& = &-2 \\\Leftrightarrow & -15x \color{red}{-5}\color{blue}{+5} & = &-2\color{blue}{+5} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)