Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-6}& = &3 \\\Leftrightarrow & 6x \color{red}{-6}\color{blue}{+6} & = &3\color{blue}{+6} \\\Leftrightarrow &6x & = &9\\\Leftrightarrow & \color{red}{6}x & = &9\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{9}{6} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & 4x \color{red}{+9}& = &9 \\\Leftrightarrow & 4x \color{red}{+9}\color{blue}{-9} & = &9\color{blue}{-9} \\\Leftrightarrow &4x & = &0\\\Leftrightarrow & \color{red}{4}x & = &0\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{0}{4} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-3}& = &8 \\\Leftrightarrow & -3x \color{red}{-3}\color{blue}{+3} & = &8\color{blue}{+3} \\\Leftrightarrow &-3x & = &11\\\Leftrightarrow & \color{red}{-3}x & = &11\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{11}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{3} } & & \\ & V = \left\{ \frac{-11}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 2x \color{red}{-7}& = &4 \\\Leftrightarrow & 2x \color{red}{-7}\color{blue}{+7} & = &4\color{blue}{+7} \\\Leftrightarrow &2x & = &11\\\Leftrightarrow & \color{red}{2}x & = &11\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{11}{2} \\\Leftrightarrow & \color{green}{ x = \frac{11}{2} } & & \\ & V = \left\{ \frac{11}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 4x \color{red}{-4}& = &-9 \\\Leftrightarrow & 4x \color{red}{-4}\color{blue}{+4} & = &-9\color{blue}{+4} \\\Leftrightarrow &4x & = &-5\\\Leftrightarrow & \color{red}{4}x & = &-5\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-5}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-5}{4} } & & \\ & V = \left\{ \frac{-5}{4} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-11}& = &10 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &10\color{blue}{+11} \\\Leftrightarrow &3x & = &21\\\Leftrightarrow & \color{red}{3}x & = &21\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{21}{3} \\\Leftrightarrow & \color{green}{ x = 7 } & & \\ & V = \left\{ 7 \right\} & \\\end{align}\)
7. \(\begin{align} & 15x \color{red}{+14}& = &5 \\\Leftrightarrow & 15x \color{red}{+14}\color{blue}{-14} & = &5\color{blue}{-14} \\\Leftrightarrow &15x & = &-9\\\Leftrightarrow & \color{red}{15}x & = &-9\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-9}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
8. \(\begin{align} & -7x \color{red}{-4}& = &-5 \\\Leftrightarrow & -7x \color{red}{-4}\color{blue}{+4} & = &-5\color{blue}{+4} \\\Leftrightarrow &-7x & = &-1\\\Leftrightarrow & \color{red}{-7}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-1}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{1}{7} } & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 8x \color{red}{-9}& = &3 \\\Leftrightarrow & 8x \color{red}{-9}\color{blue}{+9} & = &3\color{blue}{+9} \\\Leftrightarrow &8x & = &12\\\Leftrightarrow & \color{red}{8}x & = &12\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{12}{8} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
10. \(\begin{align} & 14x \color{red}{-9}& = &-15 \\\Leftrightarrow & 14x \color{red}{-9}\color{blue}{+9} & = &-15\color{blue}{+9} \\\Leftrightarrow &14x & = &-6\\\Leftrightarrow & \color{red}{14}x & = &-6\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-6}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
11. \(\begin{align} & -13x \color{red}{-5}& = &6 \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5} & = &6\color{blue}{+5} \\\Leftrightarrow &-13x & = &11\\\Leftrightarrow & \color{red}{-13}x & = &11\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{11}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{13} } & & \\ & V = \left\{ \frac{-11}{13} \right\} & \\\end{align}\)
12. \(\begin{align} & 14x \color{red}{+10}& = &-1 \\\Leftrightarrow & 14x \color{red}{+10}\color{blue}{-10} & = &-1\color{blue}{-10} \\\Leftrightarrow &14x & = &-11\\\Leftrightarrow & \color{red}{14}x & = &-11\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{-11}{14} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{14} } & & \\ & V = \left\{ \frac{-11}{14} \right\} & \\\end{align}\)