Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{+12}& = &-2 \\\Leftrightarrow & 6x \color{red}{+12}\color{blue}{-12} & = &-2\color{blue}{-12} \\\Leftrightarrow &6x & = &-14\\\Leftrightarrow & \color{red}{6}x & = &-14\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-14}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+12}& = &-10 \\\Leftrightarrow & -15x \color{red}{+12}\color{blue}{-12} & = &-10\color{blue}{-12} \\\Leftrightarrow &-15x & = &-22\\\Leftrightarrow & \color{red}{-15}x & = &-22\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-22}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{22}{15} } & & \\ & V = \left\{ \frac{22}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+4}& = &13 \\\Leftrightarrow & 12x \color{red}{+4}\color{blue}{-4} & = &13\color{blue}{-4} \\\Leftrightarrow &12x & = &9\\\Leftrightarrow & \color{red}{12}x & = &9\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{9}{12} \\\Leftrightarrow & \color{green}{ x = \frac{3}{4} } & & \\ & V = \left\{ \frac{3}{4} \right\} & \\\end{align}\)
4. \(\begin{align} & -3x \color{red}{+6}& = &6 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &6\color{blue}{-6} \\\Leftrightarrow &-3x & = &0\\\Leftrightarrow & \color{red}{-3}x & = &0\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{0}{-3} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
5. \(\begin{align} & -9x \color{red}{-10}& = &-10 \\\Leftrightarrow & -9x \color{red}{-10}\color{blue}{+10} & = &-10\color{blue}{+10} \\\Leftrightarrow &-9x & = &0\\\Leftrightarrow & \color{red}{-9}x & = &0\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{0}{-9} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
6. \(\begin{align} & -10x \color{red}{-3}& = &2 \\\Leftrightarrow & -10x \color{red}{-3}\color{blue}{+3} & = &2\color{blue}{+3} \\\Leftrightarrow &-10x & = &5\\\Leftrightarrow & \color{red}{-10}x & = &5\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{5}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{2} } & & \\ & V = \left\{ \frac{-1}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -5x \color{red}{-2}& = &15 \\\Leftrightarrow & -5x \color{red}{-2}\color{blue}{+2} & = &15\color{blue}{+2} \\\Leftrightarrow &-5x & = &17\\\Leftrightarrow & \color{red}{-5}x & = &17\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{17}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{5} } & & \\ & V = \left\{ \frac{-17}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{+12}& = &-6 \\\Leftrightarrow & -3x \color{red}{+12}\color{blue}{-12} & = &-6\color{blue}{-12} \\\Leftrightarrow &-3x & = &-18\\\Leftrightarrow & \color{red}{-3}x & = &-18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-18}{-3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
9. \(\begin{align} & -7x \color{red}{-5}& = &-12 \\\Leftrightarrow & -7x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
10. \(\begin{align} & -2x \color{red}{+8}& = &-2 \\\Leftrightarrow & -2x \color{red}{+8}\color{blue}{-8} & = &-2\color{blue}{-8} \\\Leftrightarrow &-2x & = &-10\\\Leftrightarrow & \color{red}{-2}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-10}{-2} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{+2}& = &-3 \\\Leftrightarrow & 5x \color{red}{+2}\color{blue}{-2} & = &-3\color{blue}{-2} \\\Leftrightarrow &5x & = &-5\\\Leftrightarrow & \color{red}{5}x & = &-5\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{-5}{5} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
12. \(\begin{align} & 5x \color{red}{-7}& = &-4 \\\Leftrightarrow & 5x \color{red}{-7}\color{blue}{+7} & = &-4\color{blue}{+7} \\\Leftrightarrow &5x & = &3\\\Leftrightarrow & \color{red}{5}x & = &3\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{3}{5} \\\Leftrightarrow & \color{green}{ x = \frac{3}{5} } & & \\ & V = \left\{ \frac{3}{5} \right\} & \\\end{align}\)