Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+8}& = &-7 \\\Leftrightarrow & -6x \color{red}{+8}\color{blue}{-8} & = &-7\color{blue}{-8} \\\Leftrightarrow &-6x & = &-15\\\Leftrightarrow & \color{red}{-6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-15}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{+12}& = &3 \\\Leftrightarrow & -10x \color{red}{+12}\color{blue}{-12} & = &3\color{blue}{-12} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-8}& = &1 \\\Leftrightarrow & -14x \color{red}{-8}\color{blue}{+8} & = &1\color{blue}{+8} \\\Leftrightarrow &-14x & = &9\\\Leftrightarrow & \color{red}{-14}x & = &9\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{9}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{14} } & & \\ & V = \left\{ \frac{-9}{14} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+1}& = &-13 \\\Leftrightarrow & -5x \color{red}{+1}\color{blue}{-1} & = &-13\color{blue}{-1} \\\Leftrightarrow &-5x & = &-14\\\Leftrightarrow & \color{red}{-5}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-14}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{14}{5} } & & \\ & V = \left\{ \frac{14}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -5x \color{red}{+8}& = &-9 \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8} & = &-9\color{blue}{-8} \\\Leftrightarrow &-5x & = &-17\\\Leftrightarrow & \color{red}{-5}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{17}{5} } & & \\ & V = \left\{ \frac{17}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & x \color{red}{-15}& = &6 \\\Leftrightarrow & x \color{red}{-15}\color{blue}{+15} & = &6\color{blue}{+15} \\\Leftrightarrow &x & = &21\\\Leftrightarrow & \color{red}{}x & = &21\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 21 \\\Leftrightarrow & \color{green}{ x = 21 } & & \\ & V = \left\{ 21 \right\} & \\\end{align}\)
7. \(\begin{align} & -4x \color{red}{+3}& = &15 \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3} & = &15\color{blue}{-3} \\\Leftrightarrow &-4x & = &12\\\Leftrightarrow & \color{red}{-4}x & = &12\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{12}{-4} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
8. \(\begin{align} & 5x \color{red}{-10}& = &3 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &3\color{blue}{+10} \\\Leftrightarrow &5x & = &13\\\Leftrightarrow & \color{red}{5}x & = &13\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{13}{5} \\\Leftrightarrow & \color{green}{ x = \frac{13}{5} } & & \\ & V = \left\{ \frac{13}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 13x \color{red}{+10}& = &1 \\\Leftrightarrow & 13x \color{red}{+10}\color{blue}{-10} & = &1\color{blue}{-10} \\\Leftrightarrow &13x & = &-9\\\Leftrightarrow & \color{red}{13}x & = &-9\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-9}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{13} } & & \\ & V = \left\{ \frac{-9}{13} \right\} & \\\end{align}\)
10. \(\begin{align} & -x \color{red}{+1}& = &-12 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &-x & = &-13\\\Leftrightarrow & \color{red}{-}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-13}{-1} \\\Leftrightarrow & \color{green}{ x = 13 } & & \\ & V = \left\{ 13 \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+9}& = &4 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &4\color{blue}{-9} \\\Leftrightarrow &13x & = &-5\\\Leftrightarrow & \color{red}{13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-5}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{13} } & & \\ & V = \left\{ \frac{-5}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & -5x \color{red}{+10}& = &13 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &13\color{blue}{-10} \\\Leftrightarrow &-5x & = &3\\\Leftrightarrow & \color{red}{-5}x & = &3\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{3}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)