Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -6x \color{red}{-6}& = &-10 \\\Leftrightarrow & -6x \color{red}{-6}\color{blue}{+6} & = &-10\color{blue}{+6} \\\Leftrightarrow &-6x & = &-4\\\Leftrightarrow & \color{red}{-6}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-4}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{-2}& = &8 \\\Leftrightarrow & -15x \color{red}{-2}\color{blue}{+2} & = &8\color{blue}{+2} \\\Leftrightarrow &-15x & = &10\\\Leftrightarrow & \color{red}{-15}x & = &10\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{10}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
3. \(\begin{align} & 6x \color{red}{+7}& = &1 \\\Leftrightarrow & 6x \color{red}{+7}\color{blue}{-7} & = &1\color{blue}{-7} \\\Leftrightarrow &6x & = &-6\\\Leftrightarrow & \color{red}{6}x & = &-6\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-6}{6} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{-11}& = &-1 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &-1\color{blue}{+11} \\\Leftrightarrow &3x & = &10\\\Leftrightarrow & \color{red}{3}x & = &10\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{10}{3} \\\Leftrightarrow & \color{green}{ x = \frac{10}{3} } & & \\ & V = \left\{ \frac{10}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 10x \color{red}{-14}& = &13 \\\Leftrightarrow & 10x \color{red}{-14}\color{blue}{+14} & = &13\color{blue}{+14} \\\Leftrightarrow &10x & = &27\\\Leftrightarrow & \color{red}{10}x & = &27\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{27}{10} \\\Leftrightarrow & \color{green}{ x = \frac{27}{10} } & & \\ & V = \left\{ \frac{27}{10} \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+10}& = &3 \\\Leftrightarrow & -3x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &-3x & = &-7\\\Leftrightarrow & \color{red}{-3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-7}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{7}{3} } & & \\ & V = \left\{ \frac{7}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{+11}& = &5 \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &7x & = &-6\\\Leftrightarrow & \color{red}{7}x & = &-6\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-6}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{7} } & & \\ & V = \left\{ \frac{-6}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{-6}& = &3 \\\Leftrightarrow & 7x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 12x \color{red}{-12}& = &-5 \\\Leftrightarrow & 12x \color{red}{-12}\color{blue}{+12} & = &-5\color{blue}{+12} \\\Leftrightarrow &12x & = &7\\\Leftrightarrow & \color{red}{12}x & = &7\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{7}{12} \\\Leftrightarrow & \color{green}{ x = \frac{7}{12} } & & \\ & V = \left\{ \frac{7}{12} \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-8}& = &3 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &3\color{blue}{+8} \\\Leftrightarrow &-11x & = &11\\\Leftrightarrow & \color{red}{-11}x & = &11\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{11}{-11} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
11. \(\begin{align} & -4x \color{red}{-15}& = &14 \\\Leftrightarrow & -4x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &-4x & = &29\\\Leftrightarrow & \color{red}{-4}x & = &29\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{29}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{4} } & & \\ & V = \left\{ \frac{-29}{4} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{-12}& = &3 \\\Leftrightarrow & x \color{red}{-12}\color{blue}{+12} & = &3\color{blue}{+12} \\\Leftrightarrow &x & = &15\\\Leftrightarrow & \color{red}{}x & = &15\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 15 \\\Leftrightarrow & \color{green}{ x = 15 } & & \\ & V = \left\{ 15 \right\} & \\\end{align}\)