Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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