Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 10x \color{red}{-4}& = &-6 \\\Leftrightarrow & 10x \color{red}{-4}\color{blue}{+4} & = &-6\color{blue}{+4} \\\Leftrightarrow &10x & = &-2\\\Leftrightarrow & \color{red}{10}x & = &-2\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-2}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{5} } & & \\ & V = \left\{ \frac{-1}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 5x \color{red}{-5}& = &2 \\\Leftrightarrow & 5x \color{red}{-5}\color{blue}{+5} & = &2\color{blue}{+5} \\\Leftrightarrow &5x & = &7\\\Leftrightarrow & \color{red}{5}x & = &7\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{7}{5} \\\Leftrightarrow & \color{green}{ x = \frac{7}{5} } & & \\ & V = \left\{ \frac{7}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{-10}& = &12 \\\Leftrightarrow & 12x \color{red}{-10}\color{blue}{+10} & = &12\color{blue}{+10} \\\Leftrightarrow &12x & = &22\\\Leftrightarrow & \color{red}{12}x & = &22\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{22}{12} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+6}& = &12 \\\Leftrightarrow & -7x \color{red}{+6}\color{blue}{-6} & = &12\color{blue}{-6} \\\Leftrightarrow &-7x & = &6\\\Leftrightarrow & \color{red}{-7}x & = &6\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{6}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{-10}& = &-2 \\\Leftrightarrow & -6x \color{red}{-10}\color{blue}{+10} & = &-2\color{blue}{+10} \\\Leftrightarrow &-6x & = &8\\\Leftrightarrow & \color{red}{-6}x & = &8\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{8}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 10x \color{red}{-12}& = &-4 \\\Leftrightarrow & 10x \color{red}{-12}\color{blue}{+12} & = &-4\color{blue}{+12} \\\Leftrightarrow &10x & = &8\\\Leftrightarrow & \color{red}{10}x & = &8\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{8}{10} \\\Leftrightarrow & \color{green}{ x = \frac{4}{5} } & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{+4}& = &-8 \\\Leftrightarrow & 14x \color{red}{+4}\color{blue}{-4} & = &-8\color{blue}{-4} \\\Leftrightarrow &14x & = &-12\\\Leftrightarrow & \color{red}{14}x & = &-12\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-12}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-7}& = &1 \\\Leftrightarrow & -3x \color{red}{-7}\color{blue}{+7} & = &1\color{blue}{+7} \\\Leftrightarrow &-3x & = &8\\\Leftrightarrow & \color{red}{-3}x & = &8\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{8}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
9. \(\begin{align} & 2x \color{red}{-12}& = &4 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &2x & = &16\\\Leftrightarrow & \color{red}{2}x & = &16\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{16}{2} \\\Leftrightarrow & \color{green}{ x = 8 } & & \\ & V = \left\{ 8 \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-11}& = &-8 \\\Leftrightarrow & -13x \color{red}{-11}\color{blue}{+11} & = &-8\color{blue}{+11} \\\Leftrightarrow &-13x & = &3\\\Leftrightarrow & \color{red}{-13}x & = &3\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{3}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{13} } & & \\ & V = \left\{ \frac{-3}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & -9x \color{red}{-5}& = &10 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &10\color{blue}{+5} \\\Leftrightarrow &-9x & = &15\\\Leftrightarrow & \color{red}{-9}x & = &15\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{15}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{3} } & & \\ & V = \left\{ \frac{-5}{3} \right\} & \\\end{align}\)
12. \(\begin{align} & 15x \color{red}{-3}& = &12 \\\Leftrightarrow & 15x \color{red}{-3}\color{blue}{+3} & = &12\color{blue}{+3} \\\Leftrightarrow &15x & = &15\\\Leftrightarrow & \color{red}{15}x & = &15\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{15}{15} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)