Vgln. eerste graad (reeks 1)

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Bepaal de waarde van x.

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

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Bepaal de waarde van x.

Verbetersleutel

1. \(\begin{align} & 7x \color{red}{+12}& = &-10 \\\Leftrightarrow & 7x \color{red}{+12}\color{blue}{-12} & = &-10\color{blue}{-12} \\\Leftrightarrow &7x & = &-22\\\Leftrightarrow & \color{red}{7}x & = &-22\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-22}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-22}{7} } & & \\ & V = \left\{ \frac{-22}{7} \right\} & \\\end{align}\)
2. \(\begin{align} & 9x \color{red}{+13}& = &4 \\\Leftrightarrow & 9x \color{red}{+13}\color{blue}{-13} & = &4\color{blue}{-13} \\\Leftrightarrow &9x & = &-9\\\Leftrightarrow & \color{red}{9}x & = &-9\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-9}{9} \\\Leftrightarrow & \color{green}{ x = -1 } & & \\ & V = \left\{ -1 \right\} & \\\end{align}\)
3. \(\begin{align} & 7x \color{red}{-2}& = &-10 \\\Leftrightarrow & 7x \color{red}{-2}\color{blue}{+2} & = &-10\color{blue}{+2} \\\Leftrightarrow &7x & = &-8\\\Leftrightarrow & \color{red}{7}x & = &-8\\\Leftrightarrow & \frac{\color{red}{7}x}{ \color{blue}7} & = & \frac{-8}{7} \\\Leftrightarrow & \color{green}{ x = \frac{-8}{7} } & & \\ & V = \left\{ \frac{-8}{7} \right\} & \\\end{align}\)
4. \(\begin{align} & 3x \color{red}{+4}& = &-9 \\\Leftrightarrow & 3x \color{red}{+4}\color{blue}{-4} & = &-9\color{blue}{-4} \\\Leftrightarrow &3x & = &-13\\\Leftrightarrow & \color{red}{3}x & = &-13\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{-13}{3} \\\Leftrightarrow & \color{green}{ x = \frac{-13}{3} } & & \\ & V = \left\{ \frac{-13}{3} \right\} & \\\end{align}\)
5. \(\begin{align} & 9x \color{red}{+7}& = &-9 \\\Leftrightarrow & 9x \color{red}{+7}\color{blue}{-7} & = &-9\color{blue}{-7} \\\Leftrightarrow &9x & = &-16\\\Leftrightarrow & \color{red}{9}x & = &-16\\\Leftrightarrow & \frac{\color{red}{9}x}{ \color{blue}9} & = & \frac{-16}{9} \\\Leftrightarrow & \color{green}{ x = \frac{-16}{9} } & & \\ & V = \left\{ \frac{-16}{9} \right\} & \\\end{align}\)
6. \(\begin{align} & 3x \color{red}{-11}& = &7 \\\Leftrightarrow & 3x \color{red}{-11}\color{blue}{+11} & = &7\color{blue}{+11} \\\Leftrightarrow &3x & = &18\\\Leftrightarrow & \color{red}{3}x & = &18\\\Leftrightarrow & \frac{\color{red}{3}x}{ \color{blue}3} & = & \frac{18}{3} \\\Leftrightarrow & \color{green}{ x = 6 } & & \\ & V = \left\{ 6 \right\} & \\\end{align}\)
7. \(\begin{align} & -9x \color{red}{-3}& = &-11 \\\Leftrightarrow & -9x \color{red}{-3}\color{blue}{+3} & = &-11\color{blue}{+3} \\\Leftrightarrow &-9x & = &-8\\\Leftrightarrow & \color{red}{-9}x & = &-8\\\Leftrightarrow & \frac{\color{red}{-9}x}{ \color{blue}-9} & = & \frac{-8}{-9} \\\Leftrightarrow & \color{green}{ x = \frac{8}{9} } & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
8. \(\begin{align} & -14x \color{red}{-1}& = &5 \\\Leftrightarrow & -14x \color{red}{-1}\color{blue}{+1} & = &5\color{blue}{+1} \\\Leftrightarrow &-14x & = &6\\\Leftrightarrow & \color{red}{-14}x & = &6\\\Leftrightarrow & \frac{\color{red}{-14}x}{ \color{blue}-14} & = & \frac{6}{-14} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{7} } & & \\ & V = \left\{ \frac{-3}{7} \right\} & \\\end{align}\)
9. \(\begin{align} & 11x \color{red}{-5}& = &-8 \\\Leftrightarrow & 11x \color{red}{-5}\color{blue}{+5} & = &-8\color{blue}{+5} \\\Leftrightarrow &11x & = &-3\\\Leftrightarrow & \color{red}{11}x & = &-3\\\Leftrightarrow & \frac{\color{red}{11}x}{ \color{blue}11} & = & \frac{-3}{11} \\\Leftrightarrow & \color{green}{ x = \frac{-3}{11} } & & \\ & V = \left\{ \frac{-3}{11} \right\} & \\\end{align}\)
10. \(\begin{align} & -13x \color{red}{-5}& = &-10 \\\Leftrightarrow & -13x \color{red}{-5}\color{blue}{+5} & = &-10\color{blue}{+5} \\\Leftrightarrow &-13x & = &-5\\\Leftrightarrow & \color{red}{-13}x & = &-5\\\Leftrightarrow & \frac{\color{red}{-13}x}{ \color{blue}-13} & = & \frac{-5}{-13} \\\Leftrightarrow & \color{green}{ x = \frac{5}{13} } & & \\ & V = \left\{ \frac{5}{13} \right\} & \\\end{align}\)
11. \(\begin{align} & 10x \color{red}{+9}& = &-11 \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9} & = &-11\color{blue}{-9} \\\Leftrightarrow &10x & = &-20\\\Leftrightarrow & \color{red}{10}x & = &-20\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-20}{10} \\\Leftrightarrow & \color{green}{ x = -2 } & & \\ & V = \left\{ -2 \right\} & \\\end{align}\)
12. \(\begin{align} & 10x \color{red}{+9}& = &-8 \\\Leftrightarrow & 10x \color{red}{+9}\color{blue}{-9} & = &-8\color{blue}{-9} \\\Leftrightarrow &10x & = &-17\\\Leftrightarrow & \color{red}{10}x & = &-17\\\Leftrightarrow & \frac{\color{red}{10}x}{ \color{blue}10} & = & \frac{-17}{10} \\\Leftrightarrow & \color{green}{ x = \frac{-17}{10} } & & \\ & V = \left\{ \frac{-17}{10} \right\} & \\\end{align}\)