Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 6x \color{red}{-2}& = &-3 \\\Leftrightarrow & 6x \color{red}{-2}\color{blue}{+2} & = &-3\color{blue}{+2} \\\Leftrightarrow &6x & = &-1\\\Leftrightarrow & \color{red}{6}x & = &-1\\\Leftrightarrow & \frac{\color{red}{6}x}{ \color{blue}6} & = & \frac{-1}{6} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{6} } & & \\ & V = \left\{ \frac{-1}{6} \right\} & \\\end{align}\)
2. \(\begin{align} & -15x \color{red}{+10}& = &9 \\\Leftrightarrow & -15x \color{red}{+10}\color{blue}{-10} & = &9\color{blue}{-10} \\\Leftrightarrow &-15x & = &-1\\\Leftrightarrow & \color{red}{-15}x & = &-1\\\Leftrightarrow & \frac{\color{red}{-15}x}{ \color{blue}-15} & = & \frac{-1}{-15} \\\Leftrightarrow & \color{green}{ x = \frac{1}{15} } & & \\ & V = \left\{ \frac{1}{15} \right\} & \\\end{align}\)
3. \(\begin{align} & 2x \color{red}{-15}& = &14 \\\Leftrightarrow & 2x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &2x & = &29\\\Leftrightarrow & \color{red}{2}x & = &29\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{29}{2} \\\Leftrightarrow & \color{green}{ x = \frac{29}{2} } & & \\ & V = \left\{ \frac{29}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+3}& = &-3 \\\Leftrightarrow & 4x \color{red}{+3}\color{blue}{-3} & = &-3\color{blue}{-3} \\\Leftrightarrow &4x & = &-6\\\Leftrightarrow & \color{red}{4}x & = &-6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{2} } & & \\ & V = \left\{ \frac{-3}{2} \right\} & \\\end{align}\)
5. \(\begin{align} & 11x \color{red}{-10}& = &7 \\\Leftrightarrow & 11x \color{red}{-10}\color{blue}{+10} & = &7\color{blue}{+10} \\\Leftrightarrow &11x & = &17\\\Leftrightarrow & \color{red}{11}x & = &17\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{17}{11} \\\Leftrightarrow & \color{green}{ x = \frac{17}{11} } & & \\ & V = \left\{ \frac{17}{11} \right\} & \\\end{align}\)
6. \(\begin{align} & 14x \color{red}{-2}& = &2 \\\Leftrightarrow & 14x \color{red}{-2}\color{blue}{+2} & = &2\color{blue}{+2} \\\Leftrightarrow &14x & = &4\\\Leftrightarrow & \color{red}{14}x & = &4\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{4}{14} \\\Leftrightarrow & \color{green}{ x = \frac{2}{7} } & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 14x \color{red}{-7}& = &3 \\\Leftrightarrow & 14x \color{red}{-7}\color{blue}{+7} & = &3\color{blue}{+7} \\\Leftrightarrow &14x & = &10\\\Leftrightarrow & \color{red}{14}x & = &10\\\Leftrightarrow & \frac{\color{red}{14}x}{ \color{blue}14} & = & \frac{10}{14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
8. \(\begin{align} & 3x \color{red}{-10}& = &2 \\\Leftrightarrow & 3x \color{red}{-10}\color{blue}{+10} & = &2\color{blue}{+10} \\\Leftrightarrow &3x & = &12\\\Leftrightarrow & \color{red}{3}x & = &12\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{12}{3} \\\Leftrightarrow & \color{green}{ x = 4 } & & \\ & V = \left\{ 4 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-12}& = &15 \\\Leftrightarrow & 15x \color{red}{-12}\color{blue}{+12} & = &15\color{blue}{+12} \\\Leftrightarrow &15x & = &27\\\Leftrightarrow & \color{red}{15}x & = &27\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{27}{15} \\\Leftrightarrow & \color{green}{ x = \frac{9}{5} } & & \\ & V = \left\{ \frac{9}{5} \right\} & \\\end{align}\)
10. \(\begin{align} & -12x \color{red}{+7}& = &-6 \\\Leftrightarrow & -12x \color{red}{+7}\color{blue}{-7} & = &-6\color{blue}{-7} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
11. \(\begin{align} & -6x \color{red}{+15}& = &-4 \\\Leftrightarrow & -6x \color{red}{+15}\color{blue}{-15} & = &-4\color{blue}{-15} \\\Leftrightarrow &-6x & = &-19\\\Leftrightarrow & \color{red}{-6}x & = &-19\\\Leftrightarrow & \frac{\color{red}{-6}x}{ \color{blue}-6} & = & \frac{-19}{-6} \\\Leftrightarrow & \color{green}{ x = \frac{19}{6} } & & \\ & V = \left\{ \frac{19}{6} \right\} & \\\end{align}\)
12. \(\begin{align} & -12x \color{red}{+13}& = &13 \\\Leftrightarrow & -12x \color{red}{+13}\color{blue}{-13} & = &13\color{blue}{-13} \\\Leftrightarrow &-12x & = &0\\\Leftrightarrow & \color{red}{-12}x & = &0\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{0}{-12} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)