Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -4x \color{red}{+3}& = &-14 \\\Leftrightarrow & -4x \color{red}{+3}\color{blue}{-3} & = &-14\color{blue}{-3} \\\Leftrightarrow &-4x & = &-17\\\Leftrightarrow & \color{red}{-4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{-17}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{17}{4} } & & \\ & V = \left\{ \frac{17}{4} \right\} & \\\end{align}\)
2. \(\begin{align} & 2x \color{red}{-14}& = &-10 \\\Leftrightarrow & 2x \color{red}{-14}\color{blue}{+14} & = &-10\color{blue}{+14} \\\Leftrightarrow &2x & = &4\\\Leftrightarrow & \color{red}{2}x & = &4\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{4}{2} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
3. \(\begin{align} & 10x \color{red}{+5}& = &-13 \\\Leftrightarrow & 10x \color{red}{+5}\color{blue}{-5} & = &-13\color{blue}{-5} \\\Leftrightarrow &10x & = &-18\\\Leftrightarrow & \color{red}{10}x & = &-18\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-18}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{5} } & & \\ & V = \left\{ \frac{-9}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{-11}& = &-3 \\\Leftrightarrow & -3x \color{red}{-11}\color{blue}{+11} & = &-3\color{blue}{+11} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 5x \color{red}{-3}& = &3 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &3\color{blue}{+3} \\\Leftrightarrow &5x & = &6\\\Leftrightarrow & \color{red}{5}x & = &6\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{6}{5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
6. \(\begin{align} & -9x \color{red}{-6}& = &12 \\\Leftrightarrow & -9x \color{red}{-6}\color{blue}{+6} & = &12\color{blue}{+6} \\\Leftrightarrow &-9x & = &18\\\Leftrightarrow & \color{red}{-9}x & = &18\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{18}{-9} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
7. \(\begin{align} & 2x \color{red}{-11}& = &-14 \\\Leftrightarrow & 2x \color{red}{-11}\color{blue}{+11} & = &-14\color{blue}{+11} \\\Leftrightarrow &2x & = &-3\\\Leftrightarrow & \color{red}{2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-3}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -15x \color{red}{-7}& = &-4 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &-4\color{blue}{+7} \\\Leftrightarrow &-15x & = &3\\\Leftrightarrow & \color{red}{-15}x & = &3\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{3}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -3x \color{red}{+14}& = &-11 \\\Leftrightarrow & -3x \color{red}{+14}\color{blue}{-14} & = &-11\color{blue}{-14} \\\Leftrightarrow &-3x & = &-25\\\Leftrightarrow & \color{red}{-3}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-25}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{25}{3} } & & \\ & V = \left\{ \frac{25}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{+5}& = &-1 \\\Leftrightarrow & -7x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &-7x & = &-6\\\Leftrightarrow & \color{red}{-7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{6}{7} } & & \\ & V = \left\{ \frac{6}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{-6}& = &13 \\\Leftrightarrow & 10x \color{red}{-6}\color{blue}{+6} & = &13\color{blue}{+6} \\\Leftrightarrow &10x & = &19\\\Leftrightarrow & \color{red}{10}x & = &19\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{19}{10} \\\Leftrightarrow & \color{green}{ x = \frac{19}{10} } & & \\ & V = \left\{ \frac{19}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -6x \color{red}{+2}& = &-5 \\\Leftrightarrow & -6x \color{red}{+2}\color{blue}{-2} & = &-5\color{blue}{-2} \\\Leftrightarrow &-6x & = &-7\\\Leftrightarrow & \color{red}{-6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-7}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{7}{6} } & & \\ & V = \left\{ \frac{7}{6} \right\} & \\\end{align}\)