Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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