Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -15x \color{red}{-8}& = &5 \\\Leftrightarrow & -15x \color{red}{-8}\color{blue}{+8} & = &5\color{blue}{+8} \\\Leftrightarrow &-15x & = &13\\\Leftrightarrow & \color{red}{-15}x & = &13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{15} } & & \\ & V = \left\{ \frac{-13}{15} \right\} & \\\end{align}\)
2. \(\begin{align} & 6x \color{red}{-15}& = &-1 \\\Leftrightarrow & 6x \color{red}{-15}\color{blue}{+15} & = &-1\color{blue}{+15} \\\Leftrightarrow &6x & = &14\\\Leftrightarrow & \color{red}{6}x & = &14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+12}& = &12 \\\Leftrightarrow & 10x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &10x & = &0\\\Leftrightarrow & \color{red}{10}x & = &0\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{0}{10} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{-3}& = &-4 \\\Leftrightarrow & -5x \color{red}{-3}\color{blue}{+3} & = &-4\color{blue}{+3} \\\Leftrightarrow &-5x & = &-1\\\Leftrightarrow & \color{red}{-5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-1}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{1}{5} } & & \\ & V = \left\{ \frac{1}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{-8}& = &-15 \\\Leftrightarrow & 14x \color{red}{-8}\color{blue}{+8} & = &-15\color{blue}{+8} \\\Leftrightarrow &14x & = &-7\\\Leftrightarrow & \color{red}{14}x & = &-7\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-7}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 8x \color{red}{-15}& = &-12 \\\Leftrightarrow & 8x \color{red}{-15}\color{blue}{+15} & = &-12\color{blue}{+15} \\\Leftrightarrow &8x & = &3\\\Leftrightarrow & \color{red}{8}x & = &3\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{3}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{8} } & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+9}& = &-5 \\\Leftrightarrow & 6x \color{red}{+9}\color{blue}{-9} & = &-5\color{blue}{-9} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-2}& = &9 \\\Leftrightarrow & 15x \color{red}{-2}\color{blue}{+2} & = &9\color{blue}{+2} \\\Leftrightarrow &15x & = &11\\\Leftrightarrow & \color{red}{15}x & = &11\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{11}{15} \\\Leftrightarrow & \color{green}{ x = \frac{11}{15} } & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{-1}& = &-2 \\\Leftrightarrow & -8x \color{red}{-1}\color{blue}{+1} & = &-2\color{blue}{+1} \\\Leftrightarrow &-8x & = &-1\\\Leftrightarrow & \color{red}{-8}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{8} } & & \\ & V = \left\{ \frac{1}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & 7x \color{red}{+12}& = &2 \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12} & = &2\color{blue}{-12} \\\Leftrightarrow &7x & = &-10\\\Leftrightarrow & \color{red}{7}x & = &-10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{7} } & & \\ & V = \left\{ \frac{-10}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -15x \color{red}{-11}& = &11 \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11} & = &11\color{blue}{+11} \\\Leftrightarrow &-15x & = &22\\\Leftrightarrow & \color{red}{-15}x & = &22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{15} } & & \\ & V = \left\{ \frac{-22}{15} \right\} & \\\end{align}\)
12. \(\begin{align} & 11x \color{red}{+8}& = &15 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &15\color{blue}{-8} \\\Leftrightarrow &11x & = &7\\\Leftrightarrow & \color{red}{11}x & = &7\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{7}{11} \\\Leftrightarrow & \color{green}{ x = \frac{7}{11} } & & \\ & V = \left\{ \frac{7}{11} \right\} & \\\end{align}\)