Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 13x \color{red}{+2}& = &9 \\\Leftrightarrow & 13x \color{red}{+2}\color{blue}{-2} & = &9\color{blue}{-2} \\\Leftrightarrow &13x & = &7\\\Leftrightarrow & \color{red}{13}x & = &7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{7}{13} } & & \\ & V = \left\{ \frac{7}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & 14x \color{red}{-9}& = &-15 \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9} & = &-15\color{blue}{+9} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-13}& = &15 \\\Leftrightarrow & 2x \color{red}{-13}\color{blue}{+13} & = &15\color{blue}{+13} \\\Leftrightarrow &2x & = &28\\\Leftrightarrow & \color{red}{2}x & = &28\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{28}{2} \\\Leftrightarrow & \color{green}{ x = 14 } & & \\ & V = \left\{ 14 \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{-15}& = &-8 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &-8\color{blue}{+15} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+12}& = &11 \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12} & = &11\color{blue}{-12} \\\Leftrightarrow &7x & = &-1\\\Leftrightarrow & \color{red}{7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-1}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-7}& = &2 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &2\color{blue}{+7} \\\Leftrightarrow &-10x & = &9\\\Leftrightarrow & \color{red}{-10}x & = &9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{10} } & & \\ & V = \left\{ \frac{-9}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-6}& = &7 \\\Leftrightarrow & 13x \color{red}{-6}\color{blue}{+6} & = &7\color{blue}{+6} \\\Leftrightarrow &13x & = &13\\\Leftrightarrow & \color{red}{13}x & = &13\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{13}{13} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
8. \(\begin{align} & 13x \color{red}{+1}& = &-15 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &13x & = &-16\\\Leftrightarrow & \color{red}{13}x & = &-16\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-16}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{13} } & & \\ & V = \left\{ \frac{-16}{13} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{-7}& = &-7 \\\Leftrightarrow & -9x \color{red}{-7}\color{blue}{+7} & = &-7\color{blue}{+7} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & 13x \color{red}{+1}& = &-14 \\\Leftrightarrow & 13x \color{red}{+1}\color{blue}{-1} & = &-14\color{blue}{-1} \\\Leftrightarrow &13x & = &-15\\\Leftrightarrow & \color{red}{13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-15}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-15}{13} } & & \\ & V = \left\{ \frac{-15}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-2}& = &12 \\\Leftrightarrow & 10x \color{red}{-2}\color{blue}{+2} & = &12\color{blue}{+2} \\\Leftrightarrow &10x & = &14\\\Leftrightarrow & \color{red}{10}x & = &14\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{14}{10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-3}& = &-13 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &5x & = &-10\\\Leftrightarrow & \color{red}{5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-10}{5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)