Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -9x \color{red}{+9}& = &15 \\\Leftrightarrow & -9x \color{red}{+9}\color{blue}{-9} & = &15\color{blue}{-9} \\\Leftrightarrow &-9x & = &6\\\Leftrightarrow & \color{red}{-9}x & = &6\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{6}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)
2. \(\begin{align} & -9x \color{red}{-5}& = &-12 \\\Leftrightarrow & -9x \color{red}{-5}\color{blue}{+5} & = &-12\color{blue}{+5} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
3. \(\begin{align} & -9x \color{red}{+3}& = &-4 \\\Leftrightarrow & -9x \color{red}{+3}\color{blue}{-3} & = &-4\color{blue}{-3} \\\Leftrightarrow &-9x & = &-7\\\Leftrightarrow & \color{red}{-9}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-7}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{7}{9} } & & \\ & V = \left\{ \frac{7}{9} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+6}& = &-1 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-1\color{blue}{-6} \\\Leftrightarrow &13x & = &-7\\\Leftrightarrow & \color{red}{13}x & = &-7\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-7}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{13} } & & \\ & V = \left\{ \frac{-7}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-2}& = &-11 \\\Leftrightarrow & 2x \color{red}{-2}\color{blue}{+2} & = &-11\color{blue}{+2} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
6. \(\begin{align} & -2x \color{red}{+12}& = &-13 \\\Leftrightarrow & -2x \color{red}{+12}\color{blue}{-12} & = &-13\color{blue}{-12} \\\Leftrightarrow &-2x & = &-25\\\Leftrightarrow & \color{red}{-2}x & = &-25\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-25}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{25}{2} } & & \\ & V = \left\{ \frac{25}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+1}& = &-13 \\\Leftrightarrow & -2x \color{red}{+1}\color{blue}{-1} & = &-13\color{blue}{-1} \\\Leftrightarrow &-2x & = &-14\\\Leftrightarrow & \color{red}{-2}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-14}{-2} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
8. \(\begin{align} & 15x \color{red}{+14}& = &-10 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &-10\color{blue}{-14} \\\Leftrightarrow &15x & = &-24\\\Leftrightarrow & \color{red}{15}x & = &-24\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-24}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
9. \(\begin{align} & -4x \color{red}{-1}& = &12 \\\Leftrightarrow & -4x \color{red}{-1}\color{blue}{+1} & = &12\color{blue}{+1} \\\Leftrightarrow &-4x & = &13\\\Leftrightarrow & \color{red}{-4}x & = &13\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{13}{-4} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{4} } & & \\ & V = \left\{ \frac{-13}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & -7x \color{red}{-7}& = &-14 \\\Leftrightarrow & -7x \color{red}{-7}\color{blue}{+7} & = &-14\color{blue}{+7} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{+4}& = &-11 \\\Leftrightarrow & -10x \color{red}{+4}\color{blue}{-4} & = &-11\color{blue}{-4} \\\Leftrightarrow &-10x & = &-15\\\Leftrightarrow & \color{red}{-10}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-15}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & -7x \color{red}{+8}& = &1 \\\Leftrightarrow & -7x \color{red}{+8}\color{blue}{-8} & = &1\color{blue}{-8} \\\Leftrightarrow &-7x & = &-7\\\Leftrightarrow & \color{red}{-7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-7}{-7} \\\Leftrightarrow & \color{green}{ x = 1 } & & \\ & V = \left\{ 1 \right\} & \\\end{align}\)