Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 4x \color{red}{+12}& = &-12 \\\Leftrightarrow & 4x \color{red}{+12}\color{blue}{-12} & = &-12\color{blue}{-12} \\\Leftrightarrow &4x & = &-24\\\Leftrightarrow & \color{red}{4}x & = &-24\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-24}{4} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+11}& = &-9 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &-9\color{blue}{-11} \\\Leftrightarrow &4x & = &-20\\\Leftrightarrow & \color{red}{4}x & = &-20\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-20}{4} \\\Leftrightarrow & \color{green}{ x = -5 } & & \\ & V = \left\{ -5 \right\} & \\\end{align}\)
3. \(\begin{align} & 12x \color{red}{+7}& = &13 \\\Leftrightarrow & 12x \color{red}{+7}\color{blue}{-7} & = &13\color{blue}{-7} \\\Leftrightarrow &12x & = &6\\\Leftrightarrow & \color{red}{12}x & = &6\\\Leftrightarrow & \frac{\color{red}{12}x}{ \color{blue}12} & = & \frac{6}{12} \\\Leftrightarrow & \color{green}{ x = \frac{1}{2} } & & \\ & V = \left\{ \frac{1}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & -5x \color{red}{+8}& = &-11 \\\Leftrightarrow & -5x \color{red}{+8}\color{blue}{-8} & = &-11\color{blue}{-8} \\\Leftrightarrow &-5x & = &-19\\\Leftrightarrow & \color{red}{-5}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-19}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{19}{5} } & & \\ & V = \left\{ \frac{19}{5} \right\} & \\\end{align}\)
5. \(\begin{align} & 2x \color{red}{-8}& = &10 \\\Leftrightarrow & 2x \color{red}{-8}\color{blue}{+8} & = &10\color{blue}{+8} \\\Leftrightarrow &2x & = &18\\\Leftrightarrow & \color{red}{2}x & = &18\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{18}{2} \\\Leftrightarrow & \color{green}{ x = 9 } & & \\ & V = \left\{ 9 \right\} & \\\end{align}\)
6. \(\begin{align} & 15x \color{red}{+15}& = &-9 \\\Leftrightarrow & 15x \color{red}{+15}\color{blue}{-15} & = &-9\color{blue}{-15} \\\Leftrightarrow &15x & = &-24\\\Leftrightarrow & \color{red}{15}x & = &-24\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-24}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{5} } & & \\ & V = \left\{ \frac{-8}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+5}& = &5 \\\Leftrightarrow & 15x \color{red}{+5}\color{blue}{-5} & = &5\color{blue}{-5} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+9}& = &12 \\\Leftrightarrow & -14x \color{red}{+9}\color{blue}{-9} & = &12\color{blue}{-9} \\\Leftrightarrow &-14x & = &3\\\Leftrightarrow & \color{red}{-14}x & = &3\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{3}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{14} } & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{+6}& = &-5 \\\Leftrightarrow & 8x \color{red}{+6}\color{blue}{-6} & = &-5\color{blue}{-6} \\\Leftrightarrow &8x & = &-11\\\Leftrightarrow & \color{red}{8}x & = &-11\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{-11}{8} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{8} } & & \\ & V = \left\{ \frac{-11}{8} \right\} & \\\end{align}\)
10. \(\begin{align} & -6x \color{red}{+11}& = &-2 \\\Leftrightarrow & -6x \color{red}{+11}\color{blue}{-11} & = &-2\color{blue}{-11} \\\Leftrightarrow &-6x & = &-13\\\Leftrightarrow & \color{red}{-6}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-13}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{13}{6} } & & \\ & V = \left\{ \frac{13}{6} \right\} & \\\end{align}\)
11. \(\begin{align} & 13x \color{red}{+3}& = &11 \\\Leftrightarrow & 13x \color{red}{+3}\color{blue}{-3} & = &11\color{blue}{-3} \\\Leftrightarrow &13x & = &8\\\Leftrightarrow & \color{red}{13}x & = &8\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{8}{13} \\\Leftrightarrow & \color{green}{ x = \frac{8}{13} } & & \\ & V = \left\{ \frac{8}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+5}& = &-1 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &-1\color{blue}{-5} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)