Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{+5}& = &-4 \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5} & = &-4\color{blue}{-5} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-10}& = &3 \\\Leftrightarrow & -12x \color{red}{-10}\color{blue}{+10} & = &3\color{blue}{+10} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-8}& = &-12 \\\Leftrightarrow & -9x \color{red}{-8}\color{blue}{+8} & = &-12\color{blue}{+8} \\\Leftrightarrow &-9x & = &-4\\\Leftrightarrow & \color{red}{-9}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-4}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{4}{9} } & & \\ & V = \left\{ \frac{4}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+8}& = &8 \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8} & = &8\color{blue}{-8} \\\Leftrightarrow &-5x & = &0\\\Leftrightarrow & \color{red}{-5}x & = &0\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{0}{-5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+4}& = &-12 \\\Leftrightarrow & 13x \color{red}{+4}\color{blue}{-4} & = &-12\color{blue}{-4} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{-1}& = &-9 \\\Leftrightarrow & 7x \color{red}{-1}\color{blue}{+1} & = &-9\color{blue}{+1} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+13}& = &13 \\\Leftrightarrow & 6x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &6x & = &0\\\Leftrightarrow & \color{red}{6}x & = &0\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{0}{6} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 14x \color{red}{-10}& = &-6 \\\Leftrightarrow & 14x \color{red}{-10}\color{blue}{+10} & = &-6\color{blue}{+10} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-3}& = &-15 \\\Leftrightarrow & -11x \color{red}{-3}\color{blue}{+3} & = &-15\color{blue}{+3} \\\Leftrightarrow &-11x & = &-12\\\Leftrightarrow & \color{red}{-11}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-12}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{12}{11} } & & \\ & V = \left\{ \frac{12}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 5x \color{red}{-10}& = &6 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &6\color{blue}{+10} \\\Leftrightarrow &5x & = &16\\\Leftrightarrow & \color{red}{5}x & = &16\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{16}{5} \\\Leftrightarrow & \color{green}{ x = \frac{16}{5} } & & \\ & V = \left\{ \frac{16}{5} \right\} & \\\end{align}\)
11. \(\begin{align} & 4x \color{red}{-12}& = &15 \\\Leftrightarrow & 4x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &4x & = &27\\\Leftrightarrow & \color{red}{4}x & = &27\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{27}{4} \\\Leftrightarrow & \color{green}{ x = \frac{27}{4} } & & \\ & V = \left\{ \frac{27}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & 8x \color{red}{-4}& = &14 \\\Leftrightarrow & 8x \color{red}{-4}\color{blue}{+4} & = &14\color{blue}{+4} \\\Leftrightarrow &8x & = &18\\\Leftrightarrow & \color{red}{8}x & = &18\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{18}{8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)