Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -12x \color{red}{+8}& = &3 \\\Leftrightarrow & -12x \color{red}{+8}\color{blue}{-8} & = &3\color{blue}{-8} \\\Leftrightarrow &-12x & = &-5\\\Leftrightarrow & \color{red}{-12}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-5}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{12} } & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & 11x \color{red}{+3}& = &3 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &3\color{blue}{-3} \\\Leftrightarrow &11x & = &0\\\Leftrightarrow & \color{red}{11}x & = &0\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{0}{11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{+6}& = &-15 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &-3x & = &-21\\\Leftrightarrow & \color{red}{-3}x & = &-21\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-21}{-3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+13}& = &2 \\\Leftrightarrow & 11x \color{red}{+13}\color{blue}{-13} & = &2\color{blue}{-13} \\\Leftrightarrow &11x & = &-11\\\Leftrightarrow & \color{red}{11}x & = &-11\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-11}{11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-9}& = &-5 \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9} & = &-5\color{blue}{+9} \\\Leftrightarrow &8x & = &4\\\Leftrightarrow & \color{red}{8}x & = &4\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{4}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{+13}& = &-12 \\\Leftrightarrow & -10x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &-10x & = &-25\\\Leftrightarrow & \color{red}{-10}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-25}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-8}& = &-10 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &-10\color{blue}{+8} \\\Leftrightarrow &-11x & = &-2\\\Leftrightarrow & \color{red}{-11}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-2}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-8}& = &11 \\\Leftrightarrow & -7x \color{red}{-8}\color{blue}{+8} & = &11\color{blue}{+8} \\\Leftrightarrow &-7x & = &19\\\Leftrightarrow & \color{red}{-7}x & = &19\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{19}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 9x \color{red}{+15}& = &12 \\\Leftrightarrow & 9x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &9x & = &-3\\\Leftrightarrow & \color{red}{9}x & = &-3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{+6}& = &-15 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &-15\color{blue}{-6} \\\Leftrightarrow &8x & = &-21\\\Leftrightarrow & \color{red}{8}x & = &-21\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-21}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{8} } & & \\ & V = \left\{ \frac{-21}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 8x \color{red}{+1}& = &2 \\\Leftrightarrow & 8x \color{red}{+1}\color{blue}{-1} & = &2\color{blue}{-1} \\\Leftrightarrow &8x & = &1\\\Leftrightarrow & \color{red}{8}x & = &1\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{1}{8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-4}& = &-3 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &-3\color{blue}{+4} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)