Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-13}& = &-12 \\\Leftrightarrow & x \color{red}{-13}\color{blue}{+13} & = &-12\color{blue}{+13} \\\Leftrightarrow &x & = &1\\\Leftrightarrow & \color{red}{}x & = &1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 1 \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+9}& = &-14 \\\Leftrightarrow & 9x \color{red}{+9}\color{blue}{-9} & = &-14\color{blue}{-9} \\\Leftrightarrow &9x & = &-23\\\Leftrightarrow & \color{red}{9}x & = &-23\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-23}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{9} } & & \\ & V = \left\{ \frac{-23}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+15}& = &-2 \\\Leftrightarrow & x \color{red}{+15}\color{blue}{-15} & = &-2\color{blue}{-15} \\\Leftrightarrow &x & = &-17\\\Leftrightarrow & \color{red}{}x & = &-17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -17 \\\Leftrightarrow & \color{green}{ x = -17 } & & \\ & V = \left\{ -17 \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+11}& = &-1 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &-1\color{blue}{-11} \\\Leftrightarrow &4x & = &-12\\\Leftrightarrow & \color{red}{4}x & = &-12\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-12}{4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
5. \(\begin{align} & 7x \color{red}{+3}& = &-10 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &-10\color{blue}{-3} \\\Leftrightarrow &7x & = &-13\\\Leftrightarrow & \color{red}{7}x & = &-13\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-13}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{7} } & & \\ & V = \left\{ \frac{-13}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 13x \color{red}{-4}& = &-8 \\\Leftrightarrow & 13x \color{red}{-4}\color{blue}{+4} & = &-8\color{blue}{+4} \\\Leftrightarrow &13x & = &-4\\\Leftrightarrow & \color{red}{13}x & = &-4\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-4}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{13} } & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & -7x \color{red}{+9}& = &13 \\\Leftrightarrow & -7x \color{red}{+9}\color{blue}{-9} & = &13\color{blue}{-9} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -9x \color{red}{+12}& = &-1 \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12} & = &-1\color{blue}{-12} \\\Leftrightarrow &-9x & = &-13\\\Leftrightarrow & \color{red}{-9}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-13}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{13}{9} } & & \\ & V = \left\{ \frac{13}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & 10x \color{red}{+6}& = &-12 \\\Leftrightarrow & 10x \color{red}{+6}\color{blue}{-6} & = &-12\color{blue}{-6} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -15x \color{red}{+4}& = &-9 \\\Leftrightarrow & -15x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &-15x & = &-13\\\Leftrightarrow & \color{red}{-15}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-13}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{13}{15} } & & \\ & V = \left\{ \frac{13}{15} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{+8}& = &-15 \\\Leftrightarrow & -13x \color{red}{+8}\color{blue}{-8} & = &-15\color{blue}{-8} \\\Leftrightarrow &-13x & = &-23\\\Leftrightarrow & \color{red}{-13}x & = &-23\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-23}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{23}{13} } & & \\ & V = \left\{ \frac{23}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{-4}& = &-14 \\\Leftrightarrow & 14x \color{red}{-4}\color{blue}{+4} & = &-14\color{blue}{+4} \\\Leftrightarrow &14x & = &-10\\\Leftrightarrow & \color{red}{14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{7} } & & \\ & V = \left\{ \frac{-5}{7} \right\} & \\\end{align}\)