Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-8}& = &14 \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8} & = &14\color{blue}{+8} \\\Leftrightarrow &-2x & = &22\\\Leftrightarrow & \color{red}{-2}x & = &22\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{22}{-2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-12}& = &8 \\\Leftrightarrow & -8x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &-8x & = &20\\\Leftrightarrow & \color{red}{-8}x & = &20\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{20}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+5}& = &8 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &3x & = &3\\\Leftrightarrow & \color{red}{3}x & = &3\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{3}{3} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+6}& = &-12 \\\Leftrightarrow & 11x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &11x & = &-18\\\Leftrightarrow & \color{red}{11}x & = &-18\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-18}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -4x \color{red}{-6}& = &1 \\\Leftrightarrow & -4x \color{red}{-6}\color{blue}{+6} & = &1\color{blue}{+6} \\\Leftrightarrow &-4x & = &7\\\Leftrightarrow & \color{red}{-4}x & = &7\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{7}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-10}& = &15 \\\Leftrightarrow & 10x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &10x & = &25\\\Leftrightarrow & \color{red}{10}x & = &25\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{25}{10} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-2}& = &-15 \\\Leftrightarrow & x \color{red}{-2}\color{blue}{+2} & = &-15\color{blue}{+2} \\\Leftrightarrow &x & = &-13\\\Leftrightarrow & \color{red}{}x & = &-13\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -13 \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
8. \(\begin{align} & 8x \color{red}{+14}& = &-14 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &-14\color{blue}{-14} \\\Leftrightarrow &8x & = &-28\\\Leftrightarrow & \color{red}{8}x & = &-28\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-28}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-2}& = &6 \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2} & = &6\color{blue}{+2} \\\Leftrightarrow &-12x & = &8\\\Leftrightarrow & \color{red}{-12}x & = &8\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{8}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-1}& = &-5 \\\Leftrightarrow & 12x \color{red}{-1}\color{blue}{+1} & = &-5\color{blue}{+1} \\\Leftrightarrow &12x & = &-4\\\Leftrightarrow & \color{red}{12}x & = &-4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-3}& = &-13 \\\Leftrightarrow & -7x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &-7x & = &-10\\\Leftrightarrow & \color{red}{-7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-10}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-5}& = &15 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &-9x & = &20\\\Leftrightarrow & \color{red}{-9}x & = &20\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{20}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{9} } & & \\ & V = \left\{ \frac{-20}{9} \right\} & \\\end{align}\)