Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{+12}& = &1 \\\Leftrightarrow & -6x \color{red}{+12}\color{blue}{-12} & = &1\color{blue}{-12} \\\Leftrightarrow &-6x & = &-11\\\Leftrightarrow & \color{red}{-6}x & = &-11\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-11}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -x \color{red}{-6}& = &10 \\\Leftrightarrow & -x \color{red}{-6}\color{blue}{+6} & = &10\color{blue}{+6} \\\Leftrightarrow &-x & = &16\\\Leftrightarrow & \color{red}{-}x & = &16\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{16}{-1} \\\Leftrightarrow & \color{green}{ x = -16 } & & \\ & V = \left\{ -16 \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{-10}& = &-15 \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10} & = &-15\color{blue}{+10} \\\Leftrightarrow &-9x & = &-5\\\Leftrightarrow & \color{red}{-9}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-5}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{5}{9} } & & \\ & V = \left\{ \frac{5}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{+2}& = &-4 \\\Leftrightarrow & -10x \color{red}{+2}\color{blue}{-2} & = &-4\color{blue}{-2} \\\Leftrightarrow &-10x & = &-6\\\Leftrightarrow & \color{red}{-10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-6}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & -11x \color{red}{-5}& = &12 \\\Leftrightarrow & -11x \color{red}{-5}\color{blue}{+5} & = &12\color{blue}{+5} \\\Leftrightarrow &-11x & = &17\\\Leftrightarrow & \color{red}{-11}x & = &17\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{17}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{11} } & & \\ & V = \left\{ \frac{-17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 11x \color{red}{+8}& = &13 \\\Leftrightarrow & 11x \color{red}{+8}\color{blue}{-8} & = &13\color{blue}{-8} \\\Leftrightarrow &11x & = &5\\\Leftrightarrow & \color{red}{11}x & = &5\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{5}{11} \\\Leftrightarrow & \color{green}{ x = \frac{5}{11} } & & \\ & V = \left\{ \frac{5}{11} \right\} & \\\end{align}\)
7. \(\begin{align} & x \color{red}{-12}& = &5 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &5\color{blue}{+12} \\\Leftrightarrow &x & = &17\\\Leftrightarrow & \color{red}{}x & = &17\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 17 \\\Leftrightarrow & \color{green}{ x = 17 } & & \\ & V = \left\{ 17 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{-4}& = &-9 \\\Leftrightarrow & 15x \color{red}{-4}\color{blue}{+4} & = &-9\color{blue}{+4} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & -9x \color{red}{+6}& = &5 \\\Leftrightarrow & -9x \color{red}{+6}\color{blue}{-6} & = &5\color{blue}{-6} \\\Leftrightarrow &-9x & = &-1\\\Leftrightarrow & \color{red}{-9}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-1}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{9} } & & \\ & V = \left\{ \frac{1}{9} \right\} & \\\end{align}\)
10. \(\begin{align} & -8x \color{red}{+6}& = &-10 \\\Leftrightarrow & -8x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &-8x & = &-16\\\Leftrightarrow & \color{red}{-8}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-16}{-8} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{+12}& = &-2 \\\Leftrightarrow & -9x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &-9x & = &-14\\\Leftrightarrow & \color{red}{-9}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-14}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{14}{9} } & & \\ & V = \left\{ \frac{14}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & 2x \color{red}{-15}& = &10 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &10\color{blue}{+15} \\\Leftrightarrow &2x & = &25\\\Leftrightarrow & \color{red}{2}x & = &25\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{25}{2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)