Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{-5}& = &11 \\\Leftrightarrow & -5x \color{red}{-5}\color{blue}{+5} & = &11\color{blue}{+5} \\\Leftrightarrow &-5x & = &16\\\Leftrightarrow & \color{red}{-5}x & = &16\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{16}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{5} } & & \\ & V = \left\{ \frac{-16}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & -3x \color{red}{-2}& = &13 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &13\color{blue}{+2} \\\Leftrightarrow &-3x & = &15\\\Leftrightarrow & \color{red}{-3}x & = &15\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{15}{-3} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & -12x \color{red}{-15}& = &-11 \\\Leftrightarrow & -12x \color{red}{-15}\color{blue}{+15} & = &-11\color{blue}{+15} \\\Leftrightarrow &-12x & = &4\\\Leftrightarrow & \color{red}{-12}x & = &4\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{4}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+1}& = &-12 \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+3}& = &6 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &6\color{blue}{-3} \\\Leftrightarrow &7x & = &3\\\Leftrightarrow & \color{red}{7}x & = &3\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{3}{7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -7x \color{red}{-4}& = &13 \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4} & = &13\color{blue}{+4} \\\Leftrightarrow &-7x & = &17\\\Leftrightarrow & \color{red}{-7}x & = &17\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{17}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{7} } & & \\ & V = \left\{ \frac{-17}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+13}& = &7 \\\Leftrightarrow & -3x \color{red}{+13}\color{blue}{-13} & = &7\color{blue}{-13} \\\Leftrightarrow &-3x & = &-6\\\Leftrightarrow & \color{red}{-3}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-6}{-3} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{+14}& = &5 \\\Leftrightarrow & 10x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &10x & = &-9\\\Leftrightarrow & \color{red}{10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-9}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
9. \(\begin{align} & -12x \color{red}{-12}& = &14 \\\Leftrightarrow & -12x \color{red}{-12}\color{blue}{+12} & = &14\color{blue}{+12} \\\Leftrightarrow &-12x & = &26\\\Leftrightarrow & \color{red}{-12}x & = &26\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{26}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{6} } & & \\ & V = \left\{ \frac{-13}{6} \right\} & \\\end{align}\)
10. \(\begin{align} & -14x \color{red}{-15}& = &-12 \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15} & = &-12\color{blue}{+15} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{+8}& = &1 \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8} & = &1\color{blue}{-8} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{+6}& = &6 \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6} & = &6\color{blue}{-6} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)