Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -5x \color{red}{+13}& = &11 \\\Leftrightarrow & -5x \color{red}{+13}\color{blue}{-13} & = &11\color{blue}{-13} \\\Leftrightarrow &-5x & = &-2\\\Leftrightarrow & \color{red}{-5}x & = &-2\\\Leftrightarrow & \frac{\color{red}{-5}x}{ \color{blue}-5} & = & \frac{-2}{-5} \\\Leftrightarrow & \color{green}{ x = \frac{2}{5} } & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\begin{align} & 10x \color{red}{+2}& = &-4 \\\Leftrightarrow & 10x \color{red}{+2}\color{blue}{-2} & = &-4\color{blue}{-2} \\\Leftrightarrow &10x & = &-6\\\Leftrightarrow & \color{red}{10}x & = &-6\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-6}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{5} } & & \\ & V = \left\{ \frac{-3}{5} \right\} & \\\end{align}\)
3. \(\begin{align} & 8x \color{red}{-5}& = &15 \\\Leftrightarrow & 8x \color{red}{-5}\color{blue}{+5} & = &15\color{blue}{+5} \\\Leftrightarrow &8x & = &20\\\Leftrightarrow & \color{red}{8}x & = &20\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{20}{8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{2} } & & \\ & V = \left\{ \frac{5}{2} \right\} & \\\end{align}\)
4. \(\begin{align} & 4x \color{red}{+11}& = &-6 \\\Leftrightarrow & 4x \color{red}{+11}\color{blue}{-11} & = &-6\color{blue}{-11} \\\Leftrightarrow &4x & = &-17\\\Leftrightarrow & \color{red}{4}x & = &-17\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-17}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{4} } & & \\ & V = \left\{ \frac{-17}{4} \right\} & \\\end{align}\)
5. \(\begin{align} & -14x \color{red}{+13}& = &3 \\\Leftrightarrow & -14x \color{red}{+13}\color{blue}{-13} & = &3\color{blue}{-13} \\\Leftrightarrow &-14x & = &-10\\\Leftrightarrow & \color{red}{-14}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{-10}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{5}{7} } & & \\ & V = \left\{ \frac{5}{7} \right\} & \\\end{align}\)
6. \(\begin{align} & 4x \color{red}{-14}& = &-8 \\\Leftrightarrow & 4x \color{red}{-14}\color{blue}{+14} & = &-8\color{blue}{+14} \\\Leftrightarrow &4x & = &6\\\Leftrightarrow & \color{red}{4}x & = &6\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{6}{4} \\\Leftrightarrow & \color{green}{ x = \frac{3}{2} } & & \\ & V = \left\{ \frac{3}{2} \right\} & \\\end{align}\)
7. \(\begin{align} & 13x \color{red}{+13}& = &-12 \\\Leftrightarrow & 13x \color{red}{+13}\color{blue}{-13} & = &-12\color{blue}{-13} \\\Leftrightarrow &13x & = &-25\\\Leftrightarrow & \color{red}{13}x & = &-25\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-25}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-25}{13} } & & \\ & V = \left\{ \frac{-25}{13} \right\} & \\\end{align}\)
8. \(\begin{align} & 7x \color{red}{+11}& = &4 \\\Leftrightarrow & 7x \color{red}{+11}\color{blue}{-11} & = &4\color{blue}{-11} \\\Leftrightarrow &7x & = &-7\\\Leftrightarrow & \color{red}{7}x & = &-7\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-7}{7} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
9. \(\begin{align} & 15x \color{red}{-8}& = &-8 \\\Leftrightarrow & 15x \color{red}{-8}\color{blue}{+8} & = &-8\color{blue}{+8} \\\Leftrightarrow &15x & = &0\\\Leftrightarrow & \color{red}{15}x & = &0\\\Leftrightarrow & \frac{\color{red}{15}x}{ \color{blue}15} & = & \frac{0}{15} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
10. \(\begin{align} & -11x \color{red}{-8}& = &-4 \\\Leftrightarrow & -11x \color{red}{-8}\color{blue}{+8} & = &-4\color{blue}{+8} \\\Leftrightarrow &-11x & = &4\\\Leftrightarrow & \color{red}{-11}x & = &4\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{4}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{-4}{11} } & & \\ & V = \left\{ \frac{-4}{11} \right\} & \\\end{align}\)
11. \(\begin{align} & 5x \color{red}{-3}& = &-3 \\\Leftrightarrow & 5x \color{red}{-3}\color{blue}{+3} & = &-3\color{blue}{+3} \\\Leftrightarrow &5x & = &0\\\Leftrightarrow & \color{red}{5}x & = &0\\\Leftrightarrow & \frac{\color{red}{5}x}{ \color{blue}5} & = & \frac{0}{5} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
12. \(\begin{align} & 3x \color{red}{+5}& = &-4 \\\Leftrightarrow & 3x \color{red}{+5}\color{blue}{-5} & = &-4\color{blue}{-5} \\\Leftrightarrow &3x & = &-9\\\Leftrightarrow & \color{red}{3}x & = &-9\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-9}{3} \\\Leftrightarrow & \color{green}{ x = -3 } & & \\ & V = \left\{ -3 \right\} & \\\end{align}\)