Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-12}& = &-6 \\\Leftrightarrow & 2x \color{red}{-12}\color{blue}{+12} & = &-6\color{blue}{+12} \\\Leftrightarrow &2x & = &6\\\Leftrightarrow & \color{red}{2}x & = &6\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{6}{2} \\\Leftrightarrow & \color{green}{ x = 3 } & & \\ & V = \left\{ 3 \right\} & \\\end{align}\)
2. \(\begin{align} & -8x \color{red}{-9}& = &-3 \\\Leftrightarrow & -8x \color{red}{-9}\color{blue}{+9} & = &-3\color{blue}{+9} \\\Leftrightarrow &-8x & = &6\\\Leftrightarrow & \color{red}{-8}x & = &6\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{6}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{4} } & & \\ & V = \left\{ \frac{-3}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & x \color{red}{+3}& = &-1 \\\Leftrightarrow & x \color{red}{+3}\color{blue}{-3} & = &-1\color{blue}{-3} \\\Leftrightarrow &x & = &-4\\\Leftrightarrow & \color{red}{}x & = &-4\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -4 \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
4. \(\begin{align} & -10x \color{red}{-7}& = &12 \\\Leftrightarrow & -10x \color{red}{-7}\color{blue}{+7} & = &12\color{blue}{+7} \\\Leftrightarrow &-10x & = &19\\\Leftrightarrow & \color{red}{-10}x & = &19\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{19}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{10} } & & \\ & V = \left\{ \frac{-19}{10} \right\} & \\\end{align}\)
5. \(\begin{align} & 3x \color{red}{+6}& = &-1 \\\Leftrightarrow & 3x \color{red}{+6}\color{blue}{-6} & = &-1\color{blue}{-6} \\\Leftrightarrow &3x & = &-7\\\Leftrightarrow & \color{red}{3}x & = &-7\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-7}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{3} } & & \\ & V = \left\{ \frac{-7}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & -15x \color{red}{-7}& = &5 \\\Leftrightarrow & -15x \color{red}{-7}\color{blue}{+7} & = &5\color{blue}{+7} \\\Leftrightarrow &-15x & = &12\\\Leftrightarrow & \color{red}{-15}x & = &12\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{12}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{5} } & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 6x \color{red}{+14}& = &-1 \\\Leftrightarrow & 6x \color{red}{+14}\color{blue}{-14} & = &-1\color{blue}{-14} \\\Leftrightarrow &6x & = &-15\\\Leftrightarrow & \color{red}{6}x & = &-15\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-15}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{2} } & & \\ & V = \left\{ \frac{-5}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & x \color{red}{-14}& = &11 \\\Leftrightarrow & x \color{red}{-14}\color{blue}{+14} & = &11\color{blue}{+14} \\\Leftrightarrow &x & = &25\\\Leftrightarrow & \color{red}{}x & = &25\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & 25 \\\Leftrightarrow & \color{green}{ x = 25 } & & \\ & V = \left\{ 25 \right\} & \\\end{align}\)
9. \(\begin{align} & 5x \color{red}{-10}& = &15 \\\Leftrightarrow & 5x \color{red}{-10}\color{blue}{+10} & = &15\color{blue}{+10} \\\Leftrightarrow &5x & = &25\\\Leftrightarrow & \color{red}{5}x & = &25\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{25}{5} \\\Leftrightarrow & \color{green}{ x = 5 } & & \\ & V = \left\{ 5 \right\} & \\\end{align}\)
10. \(\begin{align} & -4x \color{red}{-3}& = &5 \\\Leftrightarrow & -4x \color{red}{-3}\color{blue}{+3} & = &5\color{blue}{+3} \\\Leftrightarrow &-4x & = &8\\\Leftrightarrow & \color{red}{-4}x & = &8\\\Leftrightarrow & \frac{\color{red}{-4}x}{ \color{blue}-4} & = & \frac{8}{-4} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & -7x \color{red}{-15}& = &-7 \\\Leftrightarrow & -7x \color{red}{-15}\color{blue}{+15} & = &-7\color{blue}{+15} \\\Leftrightarrow &-7x & = &8\\\Leftrightarrow & \color{red}{-7}x & = &8\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{8}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -14x \color{red}{-9}& = &10 \\\Leftrightarrow & -14x \color{red}{-9}\color{blue}{+9} & = &10\color{blue}{+9} \\\Leftrightarrow &-14x & = &19\\\Leftrightarrow & \color{red}{-14}x & = &19\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{19}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-19}{14} } & & \\ & V = \left\{ \frac{-19}{14} \right\} & \\\end{align}\)