Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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