Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-14}& = &-14 \\\Leftrightarrow & -8x \color{red}{-14}\color{blue}{+14} & = &-14\color{blue}{+14} \\\Leftrightarrow &-8x & = &0\\\Leftrightarrow & \color{red}{-8}x & = &0\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{0}{-8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{-8}& = &8 \\\Leftrightarrow & -4x \color{red}{-8}\color{blue}{+8} & = &8\color{blue}{+8} \\\Leftrightarrow &-4x & = &16\\\Leftrightarrow & \color{red}{-4}x & = &16\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{16}{-4} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & -8x \color{red}{-12}& = &-1 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &-1\color{blue}{+12} \\\Leftrightarrow &-8x & = &11\\\Leftrightarrow & \color{red}{-8}x & = &11\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{11}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-13}& = &2 \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13} & = &2\color{blue}{+13} \\\Leftrightarrow &15x & = &15\\\Leftrightarrow & \color{red}{15}x & = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & -3x \color{red}{-7}& = &-8 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &-8\color{blue}{+7} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-9}& = &-14 \\\Leftrightarrow & -6x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &-6x & = &-5\\\Leftrightarrow & \color{red}{-6}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
7. \(\begin{align} & 9x \color{red}{+14}& = &-14 \\\Leftrightarrow & 9x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &9x & = &-28\\\Leftrightarrow & \color{red}{9}x & = &-28\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-28}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-28}{9} } & & \\ & V = \left\{ \frac{-28}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -12x \color{red}{-15}& = &-7 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &-7\color{blue}{+15} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+1}& = &-15 \\\Leftrightarrow & -3x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{-6}& = &4 \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6} & = &4\color{blue}{+6} \\\Leftrightarrow &13x & = &10\\\Leftrightarrow & \color{red}{13}x & = &10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{-2}& = &-6 \\\Leftrightarrow & -2x \color{red}{-2}\color{blue}{+2} & = &-6\color{blue}{+2} \\\Leftrightarrow &-2x & = &-4\\\Leftrightarrow & \color{red}{-2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-4}{-2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = &-12 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &-12\color{blue}{+3} \\\Leftrightarrow &-13x & = &-9\\\Leftrightarrow & \color{red}{-13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-9}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{9}{13} } & & \\ & V = \left\{ \frac{9}{13} \right\} & \\\end{align}\)