Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 8x \color{red}{+14}& = &4 \\\Leftrightarrow & 8x \color{red}{+14}\color{blue}{-14} & = &4\color{blue}{-14} \\\Leftrightarrow &8x & = &-10\\\Leftrightarrow & \color{red}{8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-10}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & x \color{red}{-9}& = &-13 \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9} & = &-13\color{blue}{+9} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{-1}& = &7 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-5x & = &8\\\Leftrightarrow & \color{red}{-5}x & = &8\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{8}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{-15}& = &11 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &11\color{blue}{+15} \\\Leftrightarrow &-12x & = &26\\\Leftrightarrow & \color{red}{-12}x & = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-3}& = &15 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &15\color{blue}{+3} \\\Leftrightarrow &-11x & = &18\\\Leftrightarrow & \color{red}{-11}x & = &18\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{18}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-18}{11} } & & \\ & V = \left\{ \frac{-18}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+14}& = &10 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &10\color{blue}{-14} \\\Leftrightarrow &-3x & = &-4\\\Leftrightarrow & \color{red}{-3}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-4}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{4}{3} } & & \\ & V = \left\{ \frac{4}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 10x \color{red}{+6}& = &2 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &10x & = &-4\\\Leftrightarrow & \color{red}{10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-4}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{5} } & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -13x \color{red}{+1}& = &-9 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-7}& = &-15 \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7} & = &-15\color{blue}{+7} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{-9}& = &4 \\\Leftrightarrow & -2x \color{red}{-9}\color{blue}{+9} & = &4\color{blue}{+9} \\\Leftrightarrow &-2x & = &13\\\Leftrightarrow & \color{red}{-2}x & = &13\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{13}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{2} } & & \\ & V = \left\{ \frac{-13}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{-8}& = &-8 \\\Leftrightarrow & 13x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &13x & = &0\\\Leftrightarrow & \color{red}{13}x & = &0\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{0}{13} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 9x \color{red}{-8}& = &-4 \\\Leftrightarrow & 9x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &9x & = &4\\\Leftrightarrow & \color{red}{9}x & = &4\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{4}{9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)