Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-8}& = &-9 \\\Leftrightarrow & -3x \color{red}{-8}\color{blue}{+8} & = &-9\color{blue}{+8} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -2x \color{red}{+6}& = &2 \\\Leftrightarrow & -2x \color{red}{+6}\color{blue}{-6} & = &2\color{blue}{-6} \\\Leftrightarrow &-2x & = &-4\\\Leftrightarrow & \color{red}{-2}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-4}{-2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+2}& = &-13 \\\Leftrightarrow & -5x \color{red}{+2}\color{blue}{-2} & = &-13\color{blue}{-2} \\\Leftrightarrow &-5x & = &-15\\\Leftrightarrow & \color{red}{-5}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-15}{-5} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & 5x \color{red}{+10}& = &-1 \\\Leftrightarrow & 5x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &5x & = &-11\\\Leftrightarrow & \color{red}{5}x & = &-11\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-11}{5} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{+15}& = &-11 \\\Leftrightarrow & -11x \color{red}{+15}\color{blue}{-15} & = &-11\color{blue}{-15} \\\Leftrightarrow &-11x & = &-26\\\Leftrightarrow & \color{red}{-11}x & = &-26\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-26}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{26}{11} } & & \\ & V = \left\{ \frac{26}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & -x \color{red}{-14}& = &-7 \\\Leftrightarrow & -x \color{red}{-14}\color{blue}{+14} & = &-7\color{blue}{+14} \\\Leftrightarrow &-x & = &7\\\Leftrightarrow & \color{red}{-}x & = &7\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{7}{-1} \\\Leftrightarrow & \color{green}{ x = -7 } & & \\ & V = \left\{ -7 \right\} & \\\end{align}\)
7. \(\begin{align} & -x \color{red}{+1}& = &5 \\\Leftrightarrow & -x \color{red}{+1}\color{blue}{-1} & = &5\color{blue}{-1} \\\Leftrightarrow &-x & = &4\\\Leftrightarrow & \color{red}{-}x & = &4\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{4}{-1} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
8. \(\begin{align} & 9x \color{red}{-4}& = &-12 \\\Leftrightarrow & 9x \color{red}{-4}\color{blue}{+4} & = &-12\color{blue}{+4} \\\Leftrightarrow &9x & = &-8\\\Leftrightarrow & \color{red}{9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-8}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{9} } & & \\ & V = \left\{ \frac{-8}{9} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{+13}& = &14 \\\Leftrightarrow & -11x \color{red}{+13}\color{blue}{-13} & = &14\color{blue}{-13} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & 8x \color{red}{-5}& = &12 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &12\color{blue}{+5} \\\Leftrightarrow &8x & = &17\\\Leftrightarrow & \color{red}{8}x & = &17\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{17}{8} \\\Leftrightarrow & \color{green}{ x = \frac{17}{8} } & & \\ & V = \left\{ \frac{17}{8} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+15}& = &-7 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &-7\color{blue}{-15} \\\Leftrightarrow &10x & = &-22\\\Leftrightarrow & \color{red}{10}x & = &-22\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-22}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{5} } & & \\ & V = \left\{ \frac{-11}{5} \right\} & \\\end{align}\)
12. \(\begin{align} & -13x \color{red}{-3}& = &-13 \\\Leftrightarrow & -13x \color{red}{-3}\color{blue}{+3} & = &-13\color{blue}{+3} \\\Leftrightarrow &-13x & = &-10\\\Leftrightarrow & \color{red}{-13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-10}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{10}{13} } & & \\ & V = \left\{ \frac{10}{13} \right\} & \\\end{align}\)