Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 12x \color{red}{+11}& = &-5 \\\Leftrightarrow & 12x \color{red}{+11}\color{blue}{-11} & = &-5\color{blue}{-11} \\\Leftrightarrow &12x & = &-16\\\Leftrightarrow & \color{red}{12}x & = &-16\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{-16}{12} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{3} } & & \\ & V = \left\{ \frac{-4}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{-2}& = &-12 \\\Leftrightarrow & -12x \color{red}{-2}\color{blue}{+2} & = &-12\color{blue}{+2} \\\Leftrightarrow &-12x & = &-10\\\Leftrightarrow & \color{red}{-12}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-10}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{5}{6} } & & \\ & V = \left\{ \frac{5}{6} \right\} & \\\end{align}\)
3. \(\begin{align} & -5x \color{red}{+11}& = &5 \\\Leftrightarrow & -5x \color{red}{+11}\color{blue}{-11} & = &5\color{blue}{-11} \\\Leftrightarrow &-5x & = &-6\\\Leftrightarrow & \color{red}{-5}x & = &-6\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-6}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{6}{5} } & & \\ & V = \left\{ \frac{6}{5} \right\} & \\\end{align}\)
4. \(\begin{align} & 7x \color{red}{+3}& = &5 \\\Leftrightarrow & 7x \color{red}{+3}\color{blue}{-3} & = &5\color{blue}{-3} \\\Leftrightarrow &7x & = &2\\\Leftrightarrow & \color{red}{7}x & = &2\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{2}{7} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & x \color{red}{+14}& = &5 \\\Leftrightarrow & x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &x & = &-9\\\Leftrightarrow & \color{red}{}x & = &-9\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -9 \\\Leftrightarrow & \color{green}{ x = -9 } & & \\ & V = \left\{ -9 \right\} & \\\end{align}\)
6. \(\begin{align} & -6x \color{red}{-12}& = &15 \\\Leftrightarrow & -6x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &-6x & = &27\\\Leftrightarrow & \color{red}{-6}x & = &27\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{27}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 7x \color{red}{-11}& = &-2 \\\Leftrightarrow & 7x \color{red}{-11}\color{blue}{+11} & = &-2\color{blue}{+11} \\\Leftrightarrow &7x & = &9\\\Leftrightarrow & \color{red}{7}x & = &9\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{9}{7} \\\Leftrightarrow & \color{green}{ x = \frac{9}{7} } & & \\ & V = \left\{ \frac{9}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & -10x \color{red}{+10}& = &6 \\\Leftrightarrow & -10x \color{red}{+10}\color{blue}{-10} & = &6\color{blue}{-10} \\\Leftrightarrow &-10x & = &-4\\\Leftrightarrow & \color{red}{-10}x & = &-4\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-4}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & 3x \color{red}{+13}& = &5 \\\Leftrightarrow & 3x \color{red}{+13}\color{blue}{-13} & = &5\color{blue}{-13} \\\Leftrightarrow &3x & = &-8\\\Leftrightarrow & \color{red}{3}x & = &-8\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-8}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{3} } & & \\ & V = \left\{ \frac{-8}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-4}& = &11 \\\Leftrightarrow & 3x \color{red}{-4}\color{blue}{+4} & = &11\color{blue}{+4} \\\Leftrightarrow &3x & = &15\\\Leftrightarrow & \color{red}{3}x & = &15\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{15}{3} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+1}& = &-2 \\\Leftrightarrow & -6x \color{red}{+1}\color{blue}{-1} & = &-2\color{blue}{-1} \\\Leftrightarrow &-6x & = &-3\\\Leftrightarrow & \color{red}{-6}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-3}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & x \color{red}{+3}& = &9 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &9\color{blue}{-3} \\\Leftrightarrow &x & = &6\\\Leftrightarrow & \color{red}{}x & = &6\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 6 \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)