Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{-15}& = &-10 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &-10\color{blue}{+15} \\\Leftrightarrow &-7x & = &5\\\Leftrightarrow & \color{red}{-7}x & = &5\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{5}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 13x \color{red}{+12}& = &11 \\\Leftrightarrow & 13x \color{red}{+12}\color{blue}{-12} & = &11\color{blue}{-12} \\\Leftrightarrow &13x & = &-1\\\Leftrightarrow & \color{red}{13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-1}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{13} } & & \\ & V = \left\{ \frac{-1}{13} \right\} & \\\end{align}\)
3. \(\begin{align} & -13x \color{red}{-5}& = &-13 \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5} & = &-13\color{blue}{+5} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
4. \(\begin{align} & -4x \color{red}{+11}& = &-4 \\\Leftrightarrow & -4x \color{red}{+11}\color{blue}{-11} & = &-4\color{blue}{-11} \\\Leftrightarrow &-4x & = &-15\\\Leftrightarrow & \color{red}{-4}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-15}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{15}{4} } & & \\ & V = \left\{ \frac{15}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{+10}& = &-14 \\\Leftrightarrow & -8x \color{red}{+10}\color{blue}{-10} & = &-14\color{blue}{-10} \\\Leftrightarrow &-8x & = &-24\\\Leftrightarrow & \color{red}{-8}x & = &-24\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-24}{-8} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-3}& = &12 \\\Leftrightarrow & 7x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &7x & = &15\\\Leftrightarrow & \color{red}{7}x & = &15\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{15}{7} \\\Leftrightarrow & \color{green}{ x = \frac{15}{7} } & & \\ & V = \left\{ \frac{15}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+9}& = &-10 \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9} & = &-10\color{blue}{-9} \\\Leftrightarrow &-4x & = &-19\\\Leftrightarrow & \color{red}{-4}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-19}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{19}{4} } & & \\ & V = \left\{ \frac{19}{4} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-5}& = &7 \\\Leftrightarrow & -14x \color{red}{-5}\color{blue}{+5} & = &7\color{blue}{+5} \\\Leftrightarrow &-14x & = &12\\\Leftrightarrow & \color{red}{-14}x & = &12\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{12}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -14x \color{red}{-1}& = &6 \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1} & = &6\color{blue}{+1} \\\Leftrightarrow &-14x & = &7\\\Leftrightarrow & \color{red}{-14}x & = &7\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{7}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{+12}& = &12 \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
11. \(\begin{align} & -x \color{red}{-4}& = &12 \\\Leftrightarrow & -x \color{red}{-4}\color{blue}{+4} & = &12\color{blue}{+4} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{+3}& = &8 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &8\color{blue}{-3} \\\Leftrightarrow &9x & = &5\\\Leftrightarrow & \color{red}{9}x & = &5\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{5}{9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)