Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 2x \color{red}{-4}& = &-11 \\\Leftrightarrow & 2x \color{red}{-4}\color{blue}{+4} & = &-11\color{blue}{+4} \\\Leftrightarrow &2x & = &-7\\\Leftrightarrow & \color{red}{2}x & = &-7\\\Leftrightarrow & \frac{\color{red}{2}x}{ \color{blue}2} & = & \frac{-7}{2} \\\Leftrightarrow & \color{green}{ x = \frac{-7}{2} } & & \\ & V = \left\{ \frac{-7}{2} \right\} & \\\end{align}\)
2. \(\begin{align} & -14x \color{red}{-15}& = &14 \\\Leftrightarrow & -14x \color{red}{-15}\color{blue}{+15} & = &14\color{blue}{+15} \\\Leftrightarrow &-14x & = &29\\\Leftrightarrow & \color{red}{-14}x & = &29\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{29}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-29}{14} } & & \\ & V = \left\{ \frac{-29}{14} \right\} & \\\end{align}\)
3. \(\begin{align} & -14x \color{red}{+4}& = &12 \\\Leftrightarrow & -14x \color{red}{+4}\color{blue}{-4} & = &12\color{blue}{-4} \\\Leftrightarrow &-14x & = &8\\\Leftrightarrow & \color{red}{-14}x & = &8\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{8}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{7} } & & \\ & V = \left\{ \frac{-4}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & -11x \color{red}{+2}& = &3 \\\Leftrightarrow & -11x \color{red}{+2}\color{blue}{-2} & = &3\color{blue}{-2} \\\Leftrightarrow &-11x & = &1\\\Leftrightarrow & \color{red}{-11}x & = &1\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{1}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{11} } & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
5. \(\begin{align} & 13x \color{red}{+6}& = &-4 \\\Leftrightarrow & 13x \color{red}{+6}\color{blue}{-6} & = &-4\color{blue}{-6} \\\Leftrightarrow &13x & = &-10\\\Leftrightarrow & \color{red}{13}x & = &-10\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-10}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-10}{13} } & & \\ & V = \left\{ \frac{-10}{13} \right\} & \\\end{align}\)
6. \(\begin{align} & 7x \color{red}{+14}& = &-9 \\\Leftrightarrow & 7x \color{red}{+14}\color{blue}{-14} & = &-9\color{blue}{-14} \\\Leftrightarrow &7x & = &-23\\\Leftrightarrow & \color{red}{7}x & = &-23\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-23}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-23}{7} } & & \\ & V = \left\{ \frac{-23}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & -2x \color{red}{+10}& = &7 \\\Leftrightarrow & -2x \color{red}{+10}\color{blue}{-10} & = &7\color{blue}{-10} \\\Leftrightarrow &-2x & = &-3\\\Leftrightarrow & \color{red}{-2}x & = &-3\\\Leftrightarrow & \frac{\color{red}{-2}x}{ \color{blue}-2} & = & \frac{-3}{-2} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
8. \(\begin{align} & -3x \color{red}{-12}& = &6 \\\Leftrightarrow & -3x \color{red}{-12}\color{blue}{+12} & = &6\color{blue}{+12} \\\Leftrightarrow &-3x & = &18\\\Leftrightarrow & \color{red}{-3}x & = &18\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{18}{-3} \\\Leftrightarrow & \color{green}{ x = -6 } & & \\ & V = \left\{ -6 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{+11}& = &6 \\\Leftrightarrow & 15x \color{red}{+11}\color{blue}{-11} & = &6\color{blue}{-11} \\\Leftrightarrow &15x & = &-5\\\Leftrightarrow & \color{red}{15}x & = &-5\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{-5}{15} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{3} } & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)
10. \(\begin{align} & 3x \color{red}{-13}& = &-11 \\\Leftrightarrow & 3x \color{red}{-13}\color{blue}{+13} & = &-11\color{blue}{+13} \\\Leftrightarrow &3x & = &2\\\Leftrightarrow & \color{red}{3}x & = &2\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{2}{3} \\\Leftrightarrow & \color{green}{ x = \frac{2}{3} } & & \\ & V = \left\{ \frac{2}{3} \right\} & \\\end{align}\)
11. \(\begin{align} & -10x \color{red}{-5}& = &6 \\\Leftrightarrow & -10x \color{red}{-5}\color{blue}{+5} & = &6\color{blue}{+5} \\\Leftrightarrow &-10x & = &11\\\Leftrightarrow & \color{red}{-10}x & = &11\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{11}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{-11}{10} } & & \\ & V = \left\{ \frac{-11}{10} \right\} & \\\end{align}\)
12. \(\begin{align} & -10x \color{red}{+11}& = &2 \\\Leftrightarrow & -10x \color{red}{+11}\color{blue}{-11} & = &2\color{blue}{-11} \\\Leftrightarrow &-10x & = &-9\\\Leftrightarrow & \color{red}{-10}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-10}x}{ \color{blue}-10} & = & \frac{-9}{-10} \\\Leftrightarrow & \color{green}{ x = \frac{9}{10} } & & \\ & V = \left\{ \frac{9}{10} \right\} & \\\end{align}\)