Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{-12}& = &-13 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &-13\color{blue}{+12} \\\Leftrightarrow &12x & = &-1\\\Leftrightarrow & \color{red}{12}x & = &-1\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-1}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{12} } & & \\ & V = \left\{ \frac{-1}{12} \right\} & \\\end{align}\)
2. \(\begin{align} & -5x \color{red}{-1}& = &9 \\\Leftrightarrow & -5x \color{red}{-1}\color{blue}{+1} & = &9\color{blue}{+1} \\\Leftrightarrow &-5x & = &10\\\Leftrightarrow & \color{red}{-5}x & = &10\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{10}{-5} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{-13}& = &9 \\\Leftrightarrow & -14x \color{red}{-13}\color{blue}{+13} & = &9\color{blue}{+13} \\\Leftrightarrow &-14x & = &22\\\Leftrightarrow & \color{red}{-14}x & = &22\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{22}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{7} } & & \\ & V = \left\{ \frac{-11}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 9x \color{red}{+8}& = &9 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &9\color{blue}{-8} \\\Leftrightarrow &9x & = &1\\\Leftrightarrow & \color{red}{9}x & = &1\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{1}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{+1}& = &-14 \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1} & = &-14\color{blue}{-1} \\\Leftrightarrow &5x & = &-15\\\Leftrightarrow & \color{red}{5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-15}{5} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)
6. \(\begin{align} & -13x \color{red}{-2}& = &-10 \\\Leftrightarrow & -13x \color{red}{-2}\color{blue}{+2} & = &-10\color{blue}{+2} \\\Leftrightarrow &-13x & = &-8\\\Leftrightarrow & \color{red}{-13}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-8}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-10}& = &5 \\\Leftrightarrow & x \color{red}{-10}\color{blue}{+10} & = &5\color{blue}{+10} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)
8. \(\begin{align} & 2x \color{red}{+9}& = &2 \\\Leftrightarrow & 2x \color{red}{+9}\color{blue}{-9} & = &2\color{blue}{-9} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{+15}& = &1 \\\Leftrightarrow & -7x \color{red}{+15}\color{blue}{-15} & = &1\color{blue}{-15} \\\Leftrightarrow &-7x & = &-14\\\Leftrightarrow & \color{red}{-7}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-14}{-7} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+4}& = &-11 \\\Leftrightarrow & -12x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &-12x & = &-15\\\Leftrightarrow & \color{red}{-12}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-15}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-11}& = &-1 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &7x & = &10\\\Leftrightarrow & \color{red}{7}x & = &10\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{10}{7} \\\Leftrightarrow & \color{green}{ x = \frac{10}{7} } & & \\ & V = \left\{ \frac{10}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -11x \color{red}{-11}& = &10 \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11} & = &10\color{blue}{+11} \\\Leftrightarrow &-11x & = &21\\\Leftrightarrow & \color{red}{-11}x & = &21\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{21}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-21}{11} } & & \\ & V = \left\{ \frac{-21}{11} \right\} & \\\end{align}\)