Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & -11x \color{red}{+1}& = &-15 \\\Leftrightarrow & -11x \color{red}{+1}\color{blue}{-1} & = &-15\color{blue}{-1} \\\Leftrightarrow &-11x & = &-16\\\Leftrightarrow & \color{red}{-11}x & = &-16\\\Leftrightarrow & \frac{\color{red}{-11}x}{ \color{blue}-11} & = & \frac{-16}{-11} \\\Leftrightarrow & \color{green}{ x = \frac{16}{11} } & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
2. \(\begin{align} & -12x \color{red}{+15}& = &2 \\\Leftrightarrow & -12x \color{red}{+15}\color{blue}{-15} & = &2\color{blue}{-15} \\\Leftrightarrow &-12x & = &-13\\\Leftrightarrow & \color{red}{-12}x & = &-13\\\Leftrightarrow & \frac{\color{red}{-12}x}{ \color{blue}-12} & = & \frac{-13}{-12} \\\Leftrightarrow & \color{green}{ x = \frac{13}{12} } & & \\ & V = \left\{ \frac{13}{12} \right\} & \\\end{align}\)
3. \(\begin{align} & -3x \color{red}{-10}& = &7 \\\Leftrightarrow & -3x \color{red}{-10}\color{blue}{+10} & = &7\color{blue}{+10} \\\Leftrightarrow &-3x & = &17\\\Leftrightarrow & \color{red}{-3}x & = &17\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{17}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{3} } & & \\ & V = \left\{ \frac{-17}{3} \right\} & \\\end{align}\)
4. \(\begin{align} & 13x \color{red}{+9}& = &3 \\\Leftrightarrow & 13x \color{red}{+9}\color{blue}{-9} & = &3\color{blue}{-9} \\\Leftrightarrow &13x & = &-6\\\Leftrightarrow & \color{red}{13}x & = &-6\\\Leftrightarrow & \frac{\color{red}{13}x}{ \color{blue}13} & = & \frac{-6}{13} \\\Leftrightarrow & \color{green}{ x = \frac{-6}{13} } & & \\ & V = \left\{ \frac{-6}{13} \right\} & \\\end{align}\)
5. \(\begin{align} & -8x \color{red}{-5}& = &-14 \\\Leftrightarrow & -8x \color{red}{-5}\color{blue}{+5} & = &-14\color{blue}{+5} \\\Leftrightarrow &-8x & = &-9\\\Leftrightarrow & \color{red}{-8}x & = &-9\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-9}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{9}{8} } & & \\ & V = \left\{ \frac{9}{8} \right\} & \\\end{align}\)
6. \(\begin{align} & -14x \color{red}{+8}& = &10 \\\Leftrightarrow & -14x \color{red}{+8}\color{blue}{-8} & = &10\color{blue}{-8} \\\Leftrightarrow &-14x & = &2\\\Leftrightarrow & \color{red}{-14}x & = &2\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{2}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-1}{7} } & & \\ & V = \left\{ \frac{-1}{7} \right\} & \\\end{align}\)
7. \(\begin{align} & 8x \color{red}{+12}& = &12 \\\Leftrightarrow & 8x \color{red}{+12}\color{blue}{-12} & = &12\color{blue}{-12} \\\Leftrightarrow &8x & = &0\\\Leftrightarrow & \color{red}{8}x & = &0\\\Leftrightarrow & \frac{\color{red}{8}x}{ \color{blue}8} & = & \frac{0}{8} \\\Leftrightarrow & \color{green}{ x = 0 } & & \\ & V = \left\{ 0 \right\} & \\\end{align}\)
8. \(\begin{align} & 4x \color{red}{+8}& = &-1 \\\Leftrightarrow & 4x \color{red}{+8}\color{blue}{-8} & = &-1\color{blue}{-8} \\\Leftrightarrow &4x & = &-9\\\Leftrightarrow & \color{red}{4}x & = &-9\\\Leftrightarrow & \frac{\color{red}{4}x}{ \color{blue}4} & = & \frac{-9}{4} \\\Leftrightarrow & \color{green}{ x = \frac{-9}{4} } & & \\ & V = \left\{ \frac{-9}{4} \right\} & \\\end{align}\)
9. \(\begin{align} & -8x \color{red}{+5}& = &-5 \\\Leftrightarrow & -8x \color{red}{+5}\color{blue}{-5} & = &-5\color{blue}{-5} \\\Leftrightarrow &-8x & = &-10\\\Leftrightarrow & \color{red}{-8}x & = &-10\\\Leftrightarrow & \frac{\color{red}{-8}x}{ \color{blue}-8} & = & \frac{-10}{-8} \\\Leftrightarrow & \color{green}{ x = \frac{5}{4} } & & \\ & V = \left\{ \frac{5}{4} \right\} & \\\end{align}\)
10. \(\begin{align} & x \color{red}{+7}& = &5 \\\Leftrightarrow & x \color{red}{+7}\color{blue}{-7} & = &5\color{blue}{-7} \\\Leftrightarrow &x & = &-2\\\Leftrightarrow & \color{red}{}x & = &-2\\\Leftrightarrow & \frac{\color{red}{}x}{ \color{blue}1} & = & -2 \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
11. \(\begin{align} & 7x \color{red}{-12}& = &14 \\\Leftrightarrow & 7x \color{red}{-12}\color{blue}{+12} & = &14\color{blue}{+12} \\\Leftrightarrow &7x & = &26\\\Leftrightarrow & \color{red}{7}x & = &26\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{26}{7} \\\Leftrightarrow & \color{green}{ x = \frac{26}{7} } & & \\ & V = \left\{ \frac{26}{7} \right\} & \\\end{align}\)
12. \(\begin{align} & -3x \color{red}{-14}& = &12 \\\Leftrightarrow & -3x \color{red}{-14}\color{blue}{+14} & = &12\color{blue}{+14} \\\Leftrightarrow &-3x & = &26\\\Leftrightarrow & \color{red}{-3}x & = &26\\\Leftrightarrow & \frac{\color{red}{-3}x}{ \color{blue}-3} & = & \frac{26}{-3} \\\Leftrightarrow & \color{green}{ x = \frac{-26}{3} } & & \\ & V = \left\{ \frac{-26}{3} \right\} & \\\end{align}\)