Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 15x \color{red}{-13}& = &-8 \\\Leftrightarrow & 15x \color{red}{-13}\color{blue}{+13} & = &-8\color{blue}{+13} \\\Leftrightarrow &15x & = &5\\\Leftrightarrow & \color{red}{15}x & = &5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+4}& = &12 \\\Leftrightarrow & 5x \color{red}{+4}\color{blue}{-4} & = &12\color{blue}{-4} \\\Leftrightarrow &5x & = &8\\\Leftrightarrow & \color{red}{5}x & = &8\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{8}{5} \\\Leftrightarrow & \color{green}{ x = \frac{8}{5} } & & \\ & V = \left\{ \frac{8}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-11}& = &5 \\\Leftrightarrow & -9x \color{red}{-11}\color{blue}{+11} & = &5\color{blue}{+11} \\\Leftrightarrow &-9x & = &16\\\Leftrightarrow & \color{red}{-9}x & = &16\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{16}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & x \color{red}{-7}& = &11 \\\Leftrightarrow & x \color{red}{-7}\color{blue}{+7} & = &11\color{blue}{+7} \\\Leftrightarrow &x & = &18\\\Leftrightarrow & \color{red}{}x & = &18\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 18 \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-7}& = &-2 \\\Leftrightarrow & -6x \color{red}{-7}\color{blue}{+7} & = &-2\color{blue}{+7} \\\Leftrightarrow &-6x & = &5\\\Leftrightarrow & \color{red}{-6}x & = &5\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{5}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{6} } & & \\ & V = \left\{ \frac{-5}{6} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-2}& = &-12 \\\Leftrightarrow & 13x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -14x \color{red}{+2}& = &2 \\\Leftrightarrow & -14x \color{red}{+2}\color{blue}{-2} & = &2\color{blue}{-2} \\\Leftrightarrow &-14x & = &0\\\Leftrightarrow & \color{red}{-14}x & = &0\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{0}{-14} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{-7}& = &5 \\\Leftrightarrow & 4x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &4x & = &12\\\Leftrightarrow & \color{red}{4}x & = &12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{12}{4} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = &-8 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &-8\color{blue}{-11} \\\Leftrightarrow &15x & = &-19\\\Leftrightarrow & \color{red}{15}x & = &-19\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-19}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{15} } & & \\ & V = \left\{ \frac{-19}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+14}& = &15 \\\Leftrightarrow & -8x \color{red}{+14}\color{blue}{-14} & = &15\color{blue}{-14} \\\Leftrightarrow &-8x & = &1\\\Leftrightarrow & \color{red}{-8}x & = &1\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{1}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{8} } & & \\ & V = \left\{ \frac{-1}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & -12x \color{red}{+5}& = &-15 \\\Leftrightarrow & -12x \color{red}{+5}\color{blue}{-5} & = &-15\color{blue}{-5} \\\Leftrightarrow &-12x & = &-20\\\Leftrightarrow & \color{red}{-12}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-20}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 7x \color{red}{+7}& = &-13 \\\Leftrightarrow & 7x \color{red}{+7}\color{blue}{-7} & = &-13\color{blue}{-7} \\\Leftrightarrow &7x & = &-20\\\Leftrightarrow & \color{red}{7}x & = &-20\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-20}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{7} } & & \\ & V = \left\{ \frac{-20}{7} \right\} & \\\end{align}\)