Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -7x \color{red}{+14}& = &10 \\\Leftrightarrow & -7x \color{red}{+14}\color{blue}{-14} & = &10\color{blue}{-14} \\\Leftrightarrow &-7x & = &-4\\\Leftrightarrow & \color{red}{-7}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & -10x \color{red}{-1}& = &7 \\\Leftrightarrow & -10x \color{red}{-1}\color{blue}{+1} & = &7\color{blue}{+1} \\\Leftrightarrow &-10x & = &8\\\Leftrightarrow & \color{red}{-10}x & = &8\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{8}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+6}& = &-4 \\\Leftrightarrow & x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &x & = &-10\\\Leftrightarrow & \color{red}{}x & = &-10\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -10 \\\Leftrightarrow & \color{green}{ x = -10 } & & \\ & V = \left\{ -10 \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-12}& = &10 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &10\color{blue}{+12} \\\Leftrightarrow &2x & = &22\\\Leftrightarrow & \color{red}{2}x & = &22\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{22}{2} \\\Leftrightarrow & \color{green}{ x = 11 } & & \\ & V = \left\{ 11 \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+14}& = &-13 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &-13\color{blue}{-14} \\\Leftrightarrow &x & = &-27\\\Leftrightarrow & \color{red}{}x & = &-27\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -27 \\\Leftrightarrow & \color{green}{ x = -27 } & & \\ & V = \left\{ -27 \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{+15}& = &6 \\\Leftrightarrow & -x \color{red}{+15}\color{blue}{-15} & = &6\color{blue}{-15} \\\Leftrightarrow &-x & = &-9\\\Leftrightarrow & \color{red}{-}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-9}{-1} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
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. \(\begin{align} & -11x \color{red}{-1}& = &15 \\\Leftrightarrow & -11x \color{red}{-1}\color{blue}{+1} & = &15\color{blue}{+1} \\\Leftrightarrow &-11x & = &16\\\Leftrightarrow & \color{red}{-11}x & = &16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{11} } & & \\ & V = \left\{ \frac{-16}{11} \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{+12}& = &11 \\\Leftrightarrow & 5x \color{red}{+12}\color{blue}{-12} & = &11\color{blue}{-12} \\\Leftrightarrow &5x & = &-1\\\Leftrightarrow & \color{red}{5}x & = &-1\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-1}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & 12x \color{red}{+9}& = &3 \\\Leftrightarrow & 12x \color{red}{+9}\color{blue}{-9} & = &3\color{blue}{-9} \\\Leftrightarrow &12x & = &-6\\\Leftrightarrow & \color{red}{12}x & = &-6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+3}& = &4 \\\Leftrightarrow & -10x \color{red}{+3}\color{blue}{-3} & = &4\color{blue}{-3} \\\Leftrightarrow &-10x & = &1\\\Leftrightarrow & \color{red}{-10}x & = &1\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{1}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{10} } & & \\ & V = \left\{ \frac{-1}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -9x \color{red}{-2}& = &-9 \\\Leftrightarrow & -9x \color{red}{-2}\color{blue}{+2} & = &-9\color{blue}{+2} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)