Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 11x \color{red}{-12}& = &-2 \\\Leftrightarrow & 11x \color{red}{-12}\color{blue}{+12} & = &-2\color{blue}{+12} \\\Leftrightarrow &11x & = &10\\\Leftrightarrow & \color{red}{11}x & = &10\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{10}{11} \\\Leftrightarrow & \color{green}{ x = \frac{10}{11} } & & \\ & V = \left\{ \frac{10}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{+5}& = &1 \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &-8x & = &-4\\\Leftrightarrow & \color{red}{-8}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-4}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{-11}& = &-4 \\\Leftrightarrow & -7x \color{red}{-11}\color{blue}{+11} & = &-4\color{blue}{+11} \\\Leftrightarrow &-7x & = &7\\\Leftrightarrow & \color{red}{-7}x & = &7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{7}{-7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{-8}& = &-11 \\\Leftrightarrow & 11x \color{red}{-8}\color{blue}{+8} & = &-11\color{blue}{+8} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-12}& = &-6 \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12} & = &-6\color{blue}{+12} \\\Leftrightarrow &-6x & = &6\\\Leftrightarrow & \color{red}{-6}x & = &6\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{6}{-6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
6. \(\begin{align} & -8x \color{red}{-15}& = &-2 \\\Leftrightarrow & -8x \color{red}{-15}\color{blue}{+15} & = &-2\color{blue}{+15} \\\Leftrightarrow &-8x & = &13\\\Leftrightarrow & \color{red}{-8}x & = &13\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{13}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{8} } & & \\ & V = \left\{ \frac{-13}{8} \right\} & \\\end{align}\)
7. \(\begin{align} & -11x \color{red}{-14}& = &9 \\\Leftrightarrow & -11x \color{red}{-14}\color{blue}{+14} & = &9\color{blue}{+14} \\\Leftrightarrow &-11x & = &23\\\Leftrightarrow & \color{red}{-11}x & = &23\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{23}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{11} } & & \\ & V = \left\{ \frac{-23}{11} \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+12}& = &7 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &7\color{blue}{-12} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-13}& = &15 \\\Leftrightarrow & 8x \color{red}{-13}\color{blue}{+13} & = &15\color{blue}{+13} \\\Leftrightarrow &8x & = &28\\\Leftrightarrow & \color{red}{8}x & = &28\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{28}{8} \\\Leftrightarrow & \color{green}{ x = \frac{7}{2} } & & \\ & V = \left\{ \frac{7}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{-10}& = &-8 \\\Leftrightarrow & 4x \color{red}{-10}\color{blue}{+10} & = &-8\color{blue}{+10} \\\Leftrightarrow &4x & = &2\\\Leftrightarrow & \color{red}{4}x & = &2\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{2}{4} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 12x \color{red}{-6}& = &6 \\\Leftrightarrow & 12x \color{red}{-6}\color{blue}{+6} & = &6\color{blue}{+6} \\\Leftrightarrow &12x & = &12\\\Leftrightarrow & \color{red}{12}x & = &12\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{12}{12} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+10}& = &3 \\\Leftrightarrow & -12x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &-12x & = &-7\\\Leftrightarrow & \color{red}{-12}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-7}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)