Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{+14}& = &5 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
2. \(\begin{align} & -4x \color{red}{+14}& = &-4 \\\Leftrightarrow & -4x \color{red}{+14}\color{blue}{-14} & = &-4\color{blue}{-14} \\\Leftrightarrow &-4x & = &-18\\\Leftrightarrow & \color{red}{-4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-18}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{9}{2} } & & \\ & V = \left\{ \frac{9}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & 4x \color{red}{+9}& = &1 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &1\color{blue}{-9} \\\Leftrightarrow &4x & = &-8\\\Leftrightarrow & \color{red}{4}x & = &-8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-8}{4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
4. \(\begin{align} & 8x \color{red}{+7}& = &15 \\\Leftrightarrow & 8x \color{red}{+7}\color{blue}{-7} & = &15\color{blue}{-7} \\\Leftrightarrow &8x & = &8\\\Leftrightarrow & \color{red}{8}x & = &8\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{8}{8} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{-1}& = &-10 \\\Leftrightarrow & 6x \color{red}{-1}\color{blue}{+1} & = &-10\color{blue}{+1} \\\Leftrightarrow &6x & = &-9\\\Leftrightarrow & \color{red}{6}x & = &-9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 6x \color{red}{-3}& = &-6 \\\Leftrightarrow & 6x \color{red}{-3}\color{blue}{+3} & = &-6\color{blue}{+3} \\\Leftrightarrow &6x & = &-3\\\Leftrightarrow & \color{red}{6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-3}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -10x \color{red}{+3}& = &10 \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3} & = &10\color{blue}{-3} \\\Leftrightarrow &-10x & = &7\\\Leftrightarrow & \color{red}{-10}x & = &7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{10} } & & \\ & V = \left\{ \frac{-7}{10} \right\} & \\\end{align}\)
8. \(\begin{align} & -11x \color{red}{+5}& = &8 \\\Leftrightarrow & -11x \color{red}{+5}\color{blue}{-5} & = &8\color{blue}{-5} \\\Leftrightarrow &-11x & = &3\\\Leftrightarrow & \color{red}{-11}x & = &3\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{3}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 7x \color{red}{+14}& = &-5 \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14} & = &-5\color{blue}{-14} \\\Leftrightarrow &7x & = &-19\\\Leftrightarrow & \color{red}{7}x & = &-19\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-19}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{7} } & & \\ & V = \left\{ \frac{-19}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & 9x \color{red}{+3}& = &-7 \\\Leftrightarrow & 9x \color{red}{+3}\color{blue}{-3} & = &-7\color{blue}{-3} \\\Leftrightarrow &9x & = &-10\\\Leftrightarrow & \color{red}{9}x & = &-10\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-10}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{9} } & & \\ & V = \left\{ \frac{-10}{9} \right\} & \\\end{align}\)
11. \(\begin{align} & -2x \color{red}{+15}& = &14 \\\Leftrightarrow & -2x \color{red}{+15}\color{blue}{-15} & = &14\color{blue}{-15} \\\Leftrightarrow &-2x & = &-1\\\Leftrightarrow & \color{red}{-2}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-1}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+2}& = &-9 \\\Leftrightarrow & 14x \color{red}{+2}\color{blue}{-2} & = &-9\color{blue}{-2} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)