Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

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