Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & x \color{red}{-5}& = &-6 \\\Leftrightarrow & x \color{red}{-5}\color{blue}{+5} & = &-6\color{blue}{+5} \\\Leftrightarrow &x & = &-1\\\Leftrightarrow & \color{red}{}x & = &-1\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -1 \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{+3}& = &2 \\\Leftrightarrow & 5x \color{red}{+3}\color{blue}{-3} & = &2\color{blue}{-3} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+10}& = &-15 \\\Leftrightarrow & -5x \color{red}{+10}\color{blue}{-10} & = &-15\color{blue}{-10} \\\Leftrightarrow &-5x & = &-25\\\Leftrightarrow & \color{red}{-5}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-25}{-5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
4. \(\begin{align} & 11x \color{red}{+3}& = &5 \\\Leftrightarrow & 11x \color{red}{+3}\color{blue}{-3} & = &5\color{blue}{-3} \\\Leftrightarrow &11x & = &2\\\Leftrightarrow & \color{red}{11}x & = &2\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{2}{11} \\\Leftrightarrow & \color{green}{ x = \frac{2}{11} } & & \\ & V = \left\{ \frac{2}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & -2x \color{red}{+14}& = &3 \\\Leftrightarrow & -2x \color{red}{+14}\color{blue}{-14} & = &3\color{blue}{-14} \\\Leftrightarrow &-2x & = &-11\\\Leftrightarrow & \color{red}{-2}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-11}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-11}& = &1 \\\Leftrightarrow & -15x \color{red}{-11}\color{blue}{+11} & = &1\color{blue}{+11} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -12x \color{red}{-1}& = &12 \\\Leftrightarrow & -12x \color{red}{-1}\color{blue}{+1} & = &12\color{blue}{+1} \\\Leftrightarrow &-12x & = &13\\\Leftrightarrow & \color{red}{-12}x & = &13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{12} } & & \\ & V = \left\{ \frac{-13}{12} \right\} & \\\end{align}\)
8. \(\begin{align} & 10x \color{red}{-5}& = &-7 \\\Leftrightarrow & 10x \color{red}{-5}\color{blue}{+5} & = &-7\color{blue}{+5} \\\Leftrightarrow &10x & = &-2\\\Leftrightarrow & \color{red}{10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+14}& = &-2 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &-2\color{blue}{-14} \\\Leftrightarrow &15x & = &-16\\\Leftrightarrow & \color{red}{15}x & = &-16\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-16}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{15} } & & \\ & V = \left\{ \frac{-16}{15} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{-11}& = &-7 \\\Leftrightarrow & 12x \color{red}{-11}\color{blue}{+11} & = &-7\color{blue}{+11} \\\Leftrightarrow &12x & = &4\\\Leftrightarrow & \color{red}{12}x & = &4\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{4}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+6}& = &6 \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6} & = &6\color{blue}{-6} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-9}& = &-13 \\\Leftrightarrow & x \color{red}{-9}\color{blue}{+9} & = &-13\color{blue}{+9} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)