Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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