Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -3x \color{red}{-2}& = &-3 \\\Leftrightarrow & -3x \color{red}{-2}\color{blue}{+2} & = &-3\color{blue}{+2} \\\Leftrightarrow &-3x & = &-1\\\Leftrightarrow & \color{red}{-3}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-1}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -7x \color{red}{-6}& = &-2 \\\Leftrightarrow & -7x \color{red}{-6}\color{blue}{+6} & = &-2\color{blue}{+6} \\\Leftrightarrow &-7x & = &4\\\Leftrightarrow & \color{red}{-7}x & = &4\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{4}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-4}& = &-13 \\\Leftrightarrow & -3x \color{red}{-4}\color{blue}{+4} & = &-13\color{blue}{+4} \\\Leftrightarrow &-3x & = &-9\\\Leftrightarrow & \color{red}{-3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-9}{-3} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
4. \(\begin{align} & -9x \color{red}{-1}& = &-3 \\\Leftrightarrow & -9x \color{red}{-1}\color{blue}{+1} & = &-3\color{blue}{+1} \\\Leftrightarrow &-9x & = &-2\\\Leftrightarrow & \color{red}{-9}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-2}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{2}{9} } & & \\ & V = \left\{ \frac{2}{9} \right\} & \\\end{align}\)
5. \(\begin{align} & 14x \color{red}{+5}& = &-11 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &-11\color{blue}{-5} \\\Leftrightarrow &14x & = &-16\\\Leftrightarrow & \color{red}{14}x & = &-16\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-16}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{+15}& = &12 \\\Leftrightarrow & 10x \color{red}{+15}\color{blue}{-15} & = &12\color{blue}{-15} \\\Leftrightarrow &10x & = &-3\\\Leftrightarrow & \color{red}{10}x & = &-3\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-3}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{10} } & & \\ & V = \left\{ \frac{-3}{10} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{-3}& = &14 \\\Leftrightarrow & 13x \color{red}{-3}\color{blue}{+3} & = &14\color{blue}{+3} \\\Leftrightarrow &13x & = &17\\\Leftrightarrow & \color{red}{13}x & = &17\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{17}{13} \\\Leftrightarrow & \color{green}{ x = \frac{17}{13} } & & \\ & V = \left\{ \frac{17}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & -x \color{red}{+3}& = &-15 \\\Leftrightarrow & -x \color{red}{+3}\color{blue}{-3} & = &-15\color{blue}{-3} \\\Leftrightarrow &-x & = &-18\\\Leftrightarrow & \color{red}{-}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-}x}{ \color{blue}-1} & = & \frac{-18}{-1} \\\Leftrightarrow & \color{green}{ x = 18 } & & \\ & V = \left\{ 18 \right\} & \\\end{align}\)
9. \(\begin{align} & -15x \color{red}{+5}& = &5 \\\Leftrightarrow & -15x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &-15x & = &0\\\Leftrightarrow & \color{red}{-15}x & = &0\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{0}{-15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-11}& = &-12 \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11} & = &-12\color{blue}{+11} \\\Leftrightarrow &-13x & = &-1\\\Leftrightarrow & \color{red}{-13}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-1}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{1}{13} } & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 9x \color{red}{-7}& = &13 \\\Leftrightarrow & 9x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &9x & = &20\\\Leftrightarrow & \color{red}{9}x & = &20\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{20}{9} \\\Leftrightarrow & \color{green}{ x = \frac{20}{9} } & & \\ & V = \left\{ \frac{20}{9} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+15}& = &8 \\\Leftrightarrow & -10x \color{red}{+15}\color{blue}{-15} & = &8\color{blue}{-15} \\\Leftrightarrow &-10x & = &-7\\\Leftrightarrow & \color{red}{-10}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-7}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{7}{10} } & & \\ & V = \left\{ \frac{7}{10} \right\} & \\\end{align}\)