Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -13x \color{red}{+1}& = &-9 \\\Leftrightarrow & -13x \color{red}{+1}\color{blue}{-1} & = &-9\color{blue}{-1} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)
2. \(\begin{align} & -11x \color{red}{+4}& = &4 \\\Leftrightarrow & -11x \color{red}{+4}\color{blue}{-4} & = &4\color{blue}{-4} \\\Leftrightarrow &-11x & = &0\\\Leftrightarrow & \color{red}{-11}x & = &0\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{0}{-11} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -7x \color{red}{+5}& = &1 \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5} & = &1\color{blue}{-5} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 15x \color{red}{+9}& = &4 \\\Leftrightarrow & 15x \color{red}{+9}\color{blue}{-9} & = &4\color{blue}{-9} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 8x \color{red}{-9}& = &10 \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &8x & = &19\\\Leftrightarrow & \color{red}{8}x & = &19\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{19}{8} \\\Leftrightarrow & \color{green}{ x = \frac{19}{8} } & & \\ & V = \left\{ \frac{19}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -12x \color{red}{-5}& = &-4 \\\Leftrightarrow & -12x \color{red}{-5}\color{blue}{+5} & = &-4\color{blue}{+5} \\\Leftrightarrow &-12x & = &1\\\Leftrightarrow & \color{red}{-12}x & = &1\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{1}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{+11}& = &1 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &1\color{blue}{-11} \\\Leftrightarrow &-5x & = &-10\\\Leftrightarrow & \color{red}{-5}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-10}{-5} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
8. \(\begin{align} & 12x \color{red}{+4}& = &3 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &3\color{blue}{-4} \\\Leftrightarrow &12x & = &-1\\\Leftrightarrow & \color{red}{12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-11}& = &14 \\\Leftrightarrow & 11x \color{red}{-11}\color{blue}{+11} & = &14\color{blue}{+11} \\\Leftrightarrow &11x & = &25\\\Leftrightarrow & \color{red}{11}x & = &25\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{25}{11} \\\Leftrightarrow & \color{green}{ x = \frac{25}{11} } & & \\ & V = \left\{ \frac{25}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 4x \color{red}{+4}& = &-10 \\\Leftrightarrow & 4x \color{red}{+4}\color{blue}{-4} & = &-10\color{blue}{-4} \\\Leftrightarrow &4x & = &-14\\\Leftrightarrow & \color{red}{4}x & = &-14\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-14}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & 3x \color{red}{-14}& = &-2 \\\Leftrightarrow & 3x \color{red}{-14}\color{blue}{+14} & = &-2\color{blue}{+14} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{-12}& = &-11 \\\Leftrightarrow & 3x \color{red}{-12}\color{blue}{+12} & = &-11\color{blue}{+12} \\\Leftrightarrow &3x & = &1\\\Leftrightarrow & \color{red}{3}x & = &1\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{1}{3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)