Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{+11}& = &-15 \\\Leftrightarrow & 2x \color{red}{+11}\color{blue}{-11} & = &-15\color{blue}{-11} \\\Leftrightarrow &2x & = &-26\\\Leftrightarrow & \color{red}{2}x & = &-26\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-26}{2} \\\Leftrightarrow & \color{green}{ x = -13 } & & \\ & V = \left\{ -13 \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+10}& = &9 \\\Leftrightarrow & 4x \color{red}{+10}\color{blue}{-10} & = &9\color{blue}{-10} \\\Leftrightarrow &4x & = &-1\\\Leftrightarrow & \color{red}{4}x & = &-1\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-1}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{4} } & & \\ & V = \left\{ \frac{-1}{4} \right\} & \\\end{align}\)
3. \(\begin{align} & 3x \color{red}{+1}& = &-12 \\\Leftrightarrow & 3x \color{red}{+1}\color{blue}{-1} & = &-12\color{blue}{-1} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 14x \color{red}{+6}& = &7 \\\Leftrightarrow & 14x \color{red}{+6}\color{blue}{-6} & = &7\color{blue}{-6} \\\Leftrightarrow &14x & = &1\\\Leftrightarrow & \color{red}{14}x & = &1\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{1}{14} \\\Leftrightarrow & \color{green}{ x = \frac{1}{14} } & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+8}& = &11 \\\Leftrightarrow & 9x \color{red}{+8}\color{blue}{-8} & = &11\color{blue}{-8} \\\Leftrightarrow &9x & = &3\\\Leftrightarrow & \color{red}{9}x & = &3\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{3}{9} \\\Leftrightarrow & \color{green}{ x = \frac{1}{3} } & & \\ & V = \left\{ \frac{1}{3} \right\} & \\\end{align}\)
6. \(\begin{align} & 5x \color{red}{+1}& = &13 \\\Leftrightarrow & 5x \color{red}{+1}\color{blue}{-1} & = &13\color{blue}{-1} \\\Leftrightarrow &5x & = &12\\\Leftrightarrow & \color{red}{5}x & = &12\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{12}{5} \\\Leftrightarrow & \color{green}{ x = \frac{12}{5} } & & \\ & V = \left\{ \frac{12}{5} \right\} & \\\end{align}\)
7. \(\begin{align} & -13x \color{red}{+6}& = &-9 \\\Leftrightarrow & -13x \color{red}{+6}\color{blue}{-6} & = &-9\color{blue}{-6} \\\Leftrightarrow &-13x & = &-15\\\Leftrightarrow & \color{red}{-13}x & = &-15\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-15}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{15}{13} } & & \\ & V = \left\{ \frac{15}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 6x \color{red}{-6}& = &5 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &5\color{blue}{+6} \\\Leftrightarrow &6x & = &11\\\Leftrightarrow & \color{red}{6}x & = &11\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{11}{6} \\\Leftrightarrow & \color{green}{ x = \frac{11}{6} } & & \\ & V = \left\{ \frac{11}{6} \right\} & \\\end{align}\)
9. \(\begin{align} & 14x \color{red}{+5}& = &-3 \\\Leftrightarrow & 14x \color{red}{+5}\color{blue}{-5} & = &-3\color{blue}{-5} \\\Leftrightarrow &14x & = &-8\\\Leftrightarrow & \color{red}{14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-8}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
10. \(\begin{align} & -5x \color{red}{-7}& = &13 \\\Leftrightarrow & -5x \color{red}{-7}\color{blue}{+7} & = &13\color{blue}{+7} \\\Leftrightarrow &-5x & = &20\\\Leftrightarrow & \color{red}{-5}x & = &20\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{20}{-5} \\\Leftrightarrow & \color{green}{ x = -4 } & & \\ & V = \left\{ -4 \right\} & \\\end{align}\)
11. \(\begin{align} & 2x \color{red}{+7}& = &-2 \\\Leftrightarrow & 2x \color{red}{+7}\color{blue}{-7} & = &-2\color{blue}{-7} \\\Leftrightarrow &2x & = &-9\\\Leftrightarrow & \color{red}{2}x & = &-9\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-9}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{2} } & & \\ & V = \left\{ \frac{-9}{2} \right\} & \\\end{align}\)
12. \(\begin{align} & 6x \color{red}{+10}& = &3 \\\Leftrightarrow & 6x \color{red}{+10}\color{blue}{-10} & = &3\color{blue}{-10} \\\Leftrightarrow &6x & = &-7\\\Leftrightarrow & \color{red}{6}x & = &-7\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-7}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{6} } & & \\ & V = \left\{ \frac{-7}{6} \right\} & \\\end{align}\)