Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -8x \color{red}{-4}& = &-14 \\\Leftrightarrow & -8x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+5}& = &13 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &13\color{blue}{-5} \\\Leftrightarrow &-15x & = &8\\\Leftrightarrow & \color{red}{-15}x & = &8\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{8}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{15} } & & \\ & V = \left\{ \frac{-8}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-7}& = &14 \\\Leftrightarrow & -12x \color{red}{-7}\color{blue}{+7} & = &14\color{blue}{+7} \\\Leftrightarrow &-12x & = &21\\\Leftrightarrow & \color{red}{-12}x & = &21\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{21}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{4} } & & \\ & V = \left\{ \frac{-7}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{-4}& = &3 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &3\color{blue}{+4} \\\Leftrightarrow &15x & = &7\\\Leftrightarrow & \color{red}{15}x & = &7\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{7}{15} \\\Leftrightarrow & \color{green}{ x = \frac{7}{15} } & & \\ & V = \left\{ \frac{7}{15} \right\} & \\\end{align}\)
5. \(\begin{align} & 6x \color{red}{+11}& = &7 \\\Leftrightarrow & 6x \color{red}{+11}\color{blue}{-11} & = &7\color{blue}{-11} \\\Leftrightarrow &6x & = &-4\\\Leftrightarrow & \color{red}{6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-4}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-12}& = &8 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &8\color{blue}{+12} \\\Leftrightarrow &3x & = &20\\\Leftrightarrow & \color{red}{3}x & = &20\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{20}{3} \\\Leftrightarrow & \color{green}{ x = \frac{20}{3} } & & \\ & V = \left\{ \frac{20}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+6}& = &-14 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &-14\color{blue}{-6} \\\Leftrightarrow &-2x & = &-20\\\Leftrightarrow & \color{red}{-2}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-20}{-2} \\\Leftrightarrow & \color{green}{ x = 10 } & & \\ & V = \left\{ 10 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-9}& = &-14 \\\Leftrightarrow & 5x \color{red}{-9}\color{blue}{+9} & = &-14\color{blue}{+9} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+1}& = &-2 \\\Leftrightarrow & 15x \color{red}{+1}\color{blue}{-1} & = &-2\color{blue}{-1} \\\Leftrightarrow &15x & = &-3\\\Leftrightarrow & \color{red}{15}x & = &-3\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-3}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{-9}& = &-8 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-8\color{blue}{+9} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -3x \color{red}{-13}& = &-13 \\\Leftrightarrow & -3x \color{red}{-13}\color{blue}{+13} & = &-13\color{blue}{+13} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & -2x \color{red}{+5}& = &-6 \\\Leftrightarrow & -2x \color{red}{+5}\color{blue}{-5} & = &-6\color{blue}{-5} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)