Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 14x \color{red}{-2}& = &3 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &3\color{blue}{+2} \\\Leftrightarrow &14x & = &5\\\Leftrightarrow & \color{red}{14}x & = &5\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{5}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{14} } & & \\ & V = \left\{ \frac{5}{14} \right\} & \\\end{align}\)
2. \(\begin{align} & 15x \color{red}{-10}& = &-4 \\\Leftrightarrow & 15x \color{red}{-10}\color{blue}{+10} & = &-4\color{blue}{+10} \\\Leftrightarrow &15x & = &6\\\Leftrightarrow & \color{red}{15}x & = &6\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{6}{15} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & -6x \color{red}{+13}& = &12 \\\Leftrightarrow & -6x \color{red}{+13}\color{blue}{-13} & = &12\color{blue}{-13} \\\Leftrightarrow &-6x & = &-1\\\Leftrightarrow & \color{red}{-6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-1}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{1}{6} } & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
4. \(\begin{align} & -7x \color{red}{+2}& = &-1 \\\Leftrightarrow & -7x \color{red}{+2}\color{blue}{-2} & = &-1\color{blue}{-2} \\\Leftrightarrow &-7x & = &-3\\\Leftrightarrow & \color{red}{-7}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-7}x}{ \color{blue}-7} & = & \frac{-3}{-7} \\\Leftrightarrow & \color{green}{ x = \frac{3}{7} } & & \\ & V = \left\{ \frac{3}{7} \right\} & \\\end{align}\)
5. \(\begin{align} & -6x \color{red}{+14}& = &2 \\\Leftrightarrow & -6x \color{red}{+14}\color{blue}{-14} & = &2\color{blue}{-14} \\\Leftrightarrow &-6x & = &-12\\\Leftrightarrow & \color{red}{-6}x & = &-12\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-12}{-6} \\\Leftrightarrow & \color{green}{ x = 2 } & & \\ & V = \left\{ 2 \right\} & \\\end{align}\)
6. \(\begin{align} & -3x \color{red}{+9}& = &-5 \\\Leftrightarrow & -3x \color{red}{+9}\color{blue}{-9} & = &-5\color{blue}{-9} \\\Leftrightarrow &-3x & = &-14\\\Leftrightarrow & \color{red}{-3}x & = &-14\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-14}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{14}{3} } & & \\ & V = \left\{ \frac{14}{3} \right\} & \\\end{align}\)
7. \(\begin{align} & -3x \color{red}{+6}& = &-10 \\\Leftrightarrow & -3x \color{red}{+6}\color{blue}{-6} & = &-10\color{blue}{-6} \\\Leftrightarrow &-3x & = &-16\\\Leftrightarrow & \color{red}{-3}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{-16}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{16}{3} } & & \\ & V = \left\{ \frac{16}{3} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{+14}& = &6 \\\Leftrightarrow & -14x \color{red}{+14}\color{blue}{-14} & = &6\color{blue}{-14} \\\Leftrightarrow &-14x & = &-8\\\Leftrightarrow & \color{red}{-14}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{4}{7} } & & \\ & V = \left\{ \frac{4}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & -11x \color{red}{-11}& = &9 \\\Leftrightarrow & -11x \color{red}{-11}\color{blue}{+11} & = &9\color{blue}{+11} \\\Leftrightarrow &-11x & = &20\\\Leftrightarrow & \color{red}{-11}x & = &20\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{20}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-20}{11} } & & \\ & V = \left\{ \frac{-20}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+12}& = &-15 \\\Leftrightarrow & -12x \color{red}{+12}\color{blue}{-12} & = &-15\color{blue}{-12} \\\Leftrightarrow &-12x & = &-27\\\Leftrightarrow & \color{red}{-12}x & = &-27\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-27}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{9}{4} } & & \\ & V = \left\{ \frac{9}{4} \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-12}& = &4 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &4\color{blue}{+12} \\\Leftrightarrow &7x & = &16\\\Leftrightarrow & \color{red}{7}x & = &16\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{16}{7} \\\Leftrightarrow & \color{green}{ x = \frac{16}{7} } & & \\ & V = \left\{ \frac{16}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+8}& = &6 \\\Leftrightarrow & 3x \color{red}{+8}\color{blue}{-8} & = &6\color{blue}{-8} \\\Leftrightarrow &3x & = &-2\\\Leftrightarrow & \color{red}{3}x & = &-2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-2}{3} } & & \\ & V = \left\{ \frac{-2}{3} \right\} & \\\end{align}\)