Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -2x \color{red}{-14}& = &8 \\\Leftrightarrow & -2x \color{red}{-14}\color{blue}{+14} & = &8\color{blue}{+14} \\\Leftrightarrow &-2x & = &22\\\Leftrightarrow & \color{red}{-2}x & = &22\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{22}{-2} \\\Leftrightarrow & \color{green}{ x = -11 } & & \\ & V = \left\{ -11 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{-4}& = &4 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &4\color{blue}{+4} \\\Leftrightarrow &4x & = &8\\\Leftrightarrow & \color{red}{4}x & = &8\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{8}{4} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -2x \color{red}{-8}& = &2 \\\Leftrightarrow & -2x \color{red}{-8}\color{blue}{+8} & = &2\color{blue}{+8} \\\Leftrightarrow &-2x & = &10\\\Leftrightarrow & \color{red}{-2}x & = &10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{10}{-2} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
4. \(\begin{align} & -12x \color{red}{+6}& = &9 \\\Leftrightarrow & -12x \color{red}{+6}\color{blue}{-6} & = &9\color{blue}{-6} \\\Leftrightarrow &-12x & = &3\\\Leftrightarrow & \color{red}{-12}x & = &3\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{3}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{+8}& = &-10 \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8} & = &-10\color{blue}{-8} \\\Leftrightarrow &4x & = &-18\\\Leftrightarrow & \color{red}{4}x & = &-18\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-18}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+11}& = &9 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &9\color{blue}{-11} \\\Leftrightarrow &15x & = &-2\\\Leftrightarrow & \color{red}{15}x & = &-2\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-2}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{15} } & & \\ & V = \left\{ \frac{-2}{15} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{+11}& = &-3 \\\Leftrightarrow & -12x \color{red}{+11}\color{blue}{-11} & = &-3\color{blue}{-11} \\\Leftrightarrow &-12x & = &-14\\\Leftrightarrow & \color{red}{-12}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-14}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)
8. \(\begin{align} & -2x \color{red}{-12}& = &-10 \\\Leftrightarrow & -2x \color{red}{-12}\color{blue}{+12} & = &-10\color{blue}{+12} \\\Leftrightarrow &-2x & = &2\\\Leftrightarrow & \color{red}{-2}x & = &2\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{2}{-2} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-11}& = &-8 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &2x & = &3\\\Leftrightarrow & \color{red}{2}x & = &3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+6}& = &-4 \\\Leftrightarrow & -6x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &-6x & = &-10\\\Leftrightarrow & \color{red}{-6}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-10}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{5}{3} } & & \\ & V = \left\{ \frac{5}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{+9}& = &-11 \\\Leftrightarrow & -4x \color{red}{+9}\color{blue}{-9} & = &-11\color{blue}{-9} \\\Leftrightarrow &-4x & = &-20\\\Leftrightarrow & \color{red}{-4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-20}{-4} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-8}& = &-12 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &-12\color{blue}{+8} \\\Leftrightarrow &-11x & = &-4\\\Leftrightarrow & \color{red}{-11}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{4}{11} } & & \\ & V = \left\{ \frac{4}{11} \right\} & \\\end{align}\)