Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-6}& = &7 \\\Leftrightarrow & -15x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 8x \color{red}{+3}& = &-13 \\\Leftrightarrow & 8x \color{red}{+3}\color{blue}{-3} & = &-13\color{blue}{-3} \\\Leftrightarrow &8x & = &-16\\\Leftrightarrow & \color{red}{8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-16}{8} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -11x \color{red}{-3}& = &12 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &-11x & = &15\\\Leftrightarrow & \color{red}{-11}x & = &15\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{15}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{11} } & & \\ & V = \left\{ \frac{-15}{11} \right\} & \\\end{align}\)
4. \(\begin{align} & -13x \color{red}{-1}& = &9 \\\Leftrightarrow & -13x \color{red}{-1}\color{blue}{+1} & = &9\color{blue}{+1} \\\Leftrightarrow &-13x & = &10\\\Leftrightarrow & \color{red}{-13}x & = &10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{+12}& = &-1 \\\Leftrightarrow & -4x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &-4x & = &-13\\\Leftrightarrow & \color{red}{-4}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{13}{4} } & & \\ & V = \left\{ \frac{13}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-14}& = &-3 \\\Leftrightarrow & 13x \color{red}{-14}\color{blue}{+14} & = &-3\color{blue}{+14} \\\Leftrightarrow &13x & = &11\\\Leftrightarrow & \color{red}{13}x & = &11\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{11}{13} \\\Leftrightarrow & \color{green}{ x = \frac{11}{13} } & & \\ & V = \left\{ \frac{11}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+9}& = &-3 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &-3\color{blue}{-9} \\\Leftrightarrow &13x & = &-12\\\Leftrightarrow & \color{red}{13}x & = &-12\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-12}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-12}{13} } & & \\ & V = \left\{ \frac{-12}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-8}& = &-3 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-3\color{blue}{+8} \\\Leftrightarrow &-3x & = &5\\\Leftrightarrow & \color{red}{-3}x & = &5\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{5}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+5}& = &-15 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &-15\color{blue}{-5} \\\Leftrightarrow &-15x & = &-20\\\Leftrightarrow & \color{red}{-15}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-20}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+14}& = &15 \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &7x & = &1\\\Leftrightarrow & \color{red}{7}x & = &1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+9}& = &-14 \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &-9x & = &-23\\\Leftrightarrow & \color{red}{-9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-23}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{23}{9} } & & \\ & V = \left\{ \frac{23}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-15}& = &7 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &7\color{blue}{+15} \\\Leftrightarrow &x & = &22\\\Leftrightarrow & \color{red}{}x & = &22\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 22 \\\Leftrightarrow & \color{green}{ x = 22 } & & \\ & V = \left\{ 22 \right\} & \\\end{align}\)