Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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